Daily Papers

Kerr nonlinear oscillators driven by a two-photon process are promising systems to encode quantum information and to ensure a hardware-efficient scaling towards fault-tolerant quantum computation. In this paper, we show that an extra control parameter, the detuning of the two-photon drive with respect to the oscillator resonance, plays a crucial role in the properties of the defined qubit. At specific values of this detuning, we benefit from strong symmetries in the system, leading to multiple degeneracies in the spectrum of the effective confinement Hamiltonian. Overall, these degeneracies lead to a stronger suppression of bit-flip errors. We also study the combination of such Hamiltonian confinement with colored dissipation to suppress leakage outside of the bosonic code space. We show that the additional degeneracies allow us to perform fast and high-fidelity gates while preserving a strong suppression of bit-flip errors.

Many machine learning algorithms rely on the Fourier transform, which is also the inner core of many analog computing devices and, specifically, of optical computing. The square of the modulus of the Fourier spectrum naturally maps onto pairwise interactions, as in the renowned Ising model, making it applicable to combinatorial optimization. Here we show how the nonlinear Fourier transform, related to integrable nonlinear partial differential equations, significantly widens the computational capability and also enables a wide variety of computing gates. We study specifically the case of the nonlinear Schrödinger equation; we introduce an input composed by ``tokens'', i.e., batches of information encoded in a multi-step potential, and we show how the nonlinear spectral computing arising in the wave propagation not only generalizes combinatorial optimization to higher order problems, but also realizes boolean gates. In the weakly nonlinear regime, nonlinearity generates higher-order interactions as perturbative corrections to the pairwise terms. In the solitonic regime, the discrete nonlinear spectrum performs digital computation through soliton generation. By using four input tokens, we demonstrate the programmability of all 256 Boolean functions of three variables, including 3-SAT instances. Our results show that integrable nonlinear propagation provides an unprecedented single physical platform for higher-order and logical computation, opening the way to a rich variety of new algorithms for analog computing, machine learning, and classical and quantum information processing.

We study a one dimensional nonlinear Klein-Gordon equation with a potential, a localized quadratic nonlinearity, and a non-localized quartic nonlinearity. We assume that the linearized operator has a single discrete eigenvalue below the continuous spectrum, corresponding to an ''internal mode''. This eigenvalue generates localized, time-periodic solutions for the linear equation. Assuming the natural Fermi Golden Rule, we give a global description of the dynamics of the amplitude of the internal mode through the radiation damping mechanism, and prove scattering for the radiation. Our approach is based on the distorted Fourier transform and a collection of refined dispersive decay and smoothing estimates. The corresponding cubic problem is closely related to the question of global-in-space dispersive asymptotics for perturbations of kink solutions in the classical ϕ^4 model, which remains a challenging open question. From the perspective of nonlinear estimates, a quartic (non-localized) interaction is essentially sharp for our analysis, and closing the estimates with such a low degree nonlinear term requires a careful and delicate treatment. As a direct application of our analysis, we prove a result on the asymptotic stability of kinks for classes of scalar field models that can be seen as perturbations of the ϕ^4 model.

We present a model for chi^{(2)} waveguides accounting for three modes, two of which make an avoided crossing at the second harmonic wavelength. We introduce two linearly coupled pure modes and adjust the coupling to replicate the waveguide dispersion near the avoided crossing. Analysis of the nonlinear system reveals continuous wave (CW) solutions across much of the parameter-space and prevalence of its modulational instability. We also predict the existence of the avoided-crossing solitons, and study peculiarities of their dynamics and spectral properties, which include formation of a pedestal in the pulse tails and associated pronounced spectral peaks. Mapping these solitons onto the linear dispersion diagrams, we make connections between their existence and CW existence and stability. We also simulate the two-color soliton generation from a single frequency pump pulse to back up its formation and stability properties.

This project focuses on a method to extract a frequency comb in mechanical means, for general interest and numerous practical applications in MEMS. The method of execution is the implementation of a beam that is exhibiting non-linear dynamics that is perturbed and analyzed for its transverse vibrations. The perturbation is an external harmonic driver with a chosen small amplitude and frequency (which is slightly detuned from the beam eigenfrequency), that when engaged with the unperturbed beam oscillations, causes it reach a state of "injection pulling" - an effect that occurs when one harmonic oscillator is coupled with a second one and causes it to oscillate in a frequency near its own. This causes the beam to reach SNIC bifurcation, rendering a frequency comb as desired. Theoretical analysis showed that the problem can be modelled using a non-linear equation of the beam, that translates to a form of the non-linear Duffing equation. While a solution to the dynamics function of the beam is hard to obtain in practice due to mathematical difficulties, a slow evolution model is suggested that is composed of functions of a amplitude and phase. Using several additional mathematical assumptions, the amplitude is seen to be related to the phase, while the phase equation solution is seen to be of the form of Adler's equation. These assumptions ultimately reduce the entire behaviour of the beam to a relatively simple solution to the Adler equation, which has a known analytical solution. Computerized numerical simulations are run on it to check the results and compare them to the theory and desired outcome. The results agreed with the theory and produce the expected frequency comb, showing the assumptions to be valid in extracting the comb.

We present an open-source Python implementation of an idealized high-order pseudo-spectral solver for the one-dimensional nonlinear Schr\"odinger equation (NLSE). The solver combines Fourier spectral spatial discretization with an adaptive eighth-order Dormand-Prince time integration scheme to achieve machine-precision conservation of mass and near-perfect preservation of momentum and energy for smooth solutions. The implementation accurately reproduces fundamental NLSE phenomena including soliton collisions with analytically predicted phase shifts, Akhmediev breather dynamics, and the development of modulation instability from noisy initial conditions. Four canonical test cases validate the numerical scheme: single soliton propagation, two-soliton elastic collision, breather evolution, and noise-seeded modulation instability. The solver employs a 2/3 dealiasing rule with exponential filtering to prevent aliasing errors from the cubic nonlinearity. Statistical analysis using Shannon, R\'enyi, and Tsallis entropies quantifies the spatio-temporal complexity of solutions, while phase space representations reveal the underlying coherence structure. The implementation prioritizes code transparency and educational accessibility over computational performance, providing a valuable pedagogical tool for exploring nonlinear wave dynamics. Complete source code, documentation, and example configurations are freely available, enabling reproducible computational experiments across diverse physical contexts where the NLSE governs wave evolution, including nonlinear optics, Bose-Einstein condensates, and ocean surface waves.

We construct Feynman rules for Lindblad master equations in the operator language of quantum optics: a fixed algebra of elementary operator moves and closed-form propagators for perturbation theory about an exactly solvable, in most cases Gaussian, generator. The expansion separates into a kinematic part (the shift algebra on the Wick-ordered eigenoperators O_{mn}=:(c^dagger)^m c^n:, from which the vertex table for a specified interaction is assembled) and a dynamical part that enters only through the resolvent of the unperturbed generator, diagonal and additive for any stable, diagonalizable Gaussian L_0, including thermal and squeezed reservoirs and correlated decay, and equally available for a two-level emitter, driven or undriven. In the driven Kerr cavity the loop expansion is the semiclassical expansion and the series is asymptotic. In a strongly driven two-level atom, dressed lines replace a series of finite radius by one accurate deep into saturation, one line per Mollow component. For Kerr rings and chains the cost is polynomial in the number of sites at fixed perturbative order. On a three-site ring the diagrams recover the non-Gaussian part of the three-photon correlation that the Gaussian cumulant closure lacks; carried to tenth order they give the smallest g^{(3)} error of the methods compared for Uleq0.25κ at a cost below that of a fourth-order closure, and third- and fourth-order closures are more accurate at moderate coupling. The same rules, extended to the counting-field-tilted generator, give the photon-counting cumulants of a disordered eight-site chain beyond direct diagonalization; quantum-jump trajectories at three couplings agree with them to within 1.6 standard errors, within one at the strongest coupling, where they place the third cumulant six standard errors above the Gaussian value.

Cavity optomechanical systems in the quantum regime consist of a cavity mode and mechanical element coupled together through radiation pressure. In the nonlinear optomechanical regime, open-system dynamics is generally challenging to treat analytically, since the noise terms do not commute with the optomechanical interaction term. Specifically, a general treatment of both Markovian and non-Markovian mechanical noise in the nonlinear optomechanical regime is still outstanding. Here we address this question by solving the full dynamics of an optomechanical system in the nonlinear regime where the mechanical element interacts with a bath of harmonic oscillators, representing full quantum Brownian motion. The solutions, which are exact and analytic, allow us to consider the strength of the optomechanical nonlinearity in the presence of both Markovian (Ohmic) and non-Markovian (sub-Ohmic and super-Ohmic) baths. We show that that while the strength of the nonlinearity is generally reduced by a Markovian bath spectrum, it can be enhanced by constructing a bath with a highly non-Markovian structure. The results have potential implications for future optomechanical experiments which seek to achieve a strong optomechanical nonlinearity.

The non-linear gravitational-wave memory effect is a prediction of general relativity in which test masses are permanently displaced by gravitational radiation. We implement a method for calculating the expected memory waveform from an oscillatory gravitational-wave time series. We use this method to explore the phenomenology of gravitational-wave memory using a numerical relativity surrogate model. Previous methods of calculating the memory have considered only the dominant oscillatory (ell=2, m=|2|) mode in the spherical harmonic decomposition or the post-Newtonian expansion. We explore the contribution of higher-order modes and reveal a richer phenomenology than is apparent with ell=|m|=2 modes alone. We also consider the `memory of the memory' in which the memory is, itself, a source of memory, which leads to a small, Oleft(10^{-4}right), correction to the memory waveform. The method is implemented in the python package {\tt\sc GWMemory}, which is made publicly available.

Quantum error correction with biased-noise qubits can drastically reduce the hardware overhead for universal and fault-tolerant quantum computation. Cat qubits are a promising realization of biased-noise qubits as they feature an exponential error bias inherited from their non-local encoding in the phase space of a quantum harmonic oscillator. To confine the state of an oscillator to the cat qubit manifold, two main approaches have been considered so far: a Kerr-based Hamiltonian confinement with high gate performances, and a dissipative confinement with robust protection against a broad range of noise mechanisms. We introduce a new combined dissipative and Hamiltonian confinement scheme based on two-photon dissipation together with a Two-Photon Exchange (TPE) Hamiltonian. The TPE Hamiltonian is similar to Kerr nonlinearity, but unlike the Kerr it only induces a bounded distinction between even- and odd-photon eigenstates, a highly beneficial feature for protecting the cat qubits with dissipative mechanisms. Using this combined confinement scheme, we demonstrate fast and bias-preserving gates with drastically improved performance compared to dissipative or Hamiltonian schemes. In addition, this combined scheme can be implemented experimentally with only minor modifications of existing dissipative cat qubit experiments.

This review presents recent breakthroughs in the realm of nonlinear Hall effects, emphasizing central theoretical foundations and recent experimental progress. We elucidate the quantum origin of the second-order Hall response, focusing on the Berry curvature dipole, which may arise in inversion symmetry broken systems. The theoretical framework also reveals the impact of disorder scattering effects on the nonlinear response. We further discuss the possibility of obtaining nonlinear Hall responses beyond the second order. We examine symmetry-based indicators essential for the manifestation of nonlinear Hall effects in time-reversal symmetric crystals, setting the stage for a detailed exploration of theoretical models and candidate materials predicted to exhibit sizable and tunable Berry curvature dipole. We summarize groundbreaking experimental reports on measuring both intrinsic and extrinsic nonlinear Hall effects across diverse material classes. Finally, we highlight some of the other intriguing nonlinear effects, including nonlinear planar Hall, nonlinear anomalous Hall, and nonlinear spin and valley Hall effects. We conclude with an outlook on pivotal open questions and challenges, marking the trajectory of this rapidly evolving field.

Existing model reduction techniques for high-dimensional models of conservative partial differential equations (PDEs) encounter computational bottlenecks when dealing with systems featuring non-polynomial nonlinearities. This work presents a nonlinear model reduction method that employs lifting variable transformations to derive structure-preserving quadratic reduced-order models for conservative PDEs with general nonlinearities. We present an energy-quadratization strategy that defines the auxiliary variable in terms of the nonlinear term in the energy expression to derive an equivalent quadratic lifted system with quadratic system energy. The proposed strategy combined with proper orthogonal decomposition model reduction yields quadratic reduced-order models that conserve the quadratized lifted energy exactly in high dimensions. We demonstrate the proposed model reduction approach on four nonlinear conservative PDEs: the one-dimensional wave equation with exponential nonlinearity, the two-dimensional sine-Gordon equation, the two-dimensional Klein-Gordon equation with parametric dependence, and the two-dimensional Klein-Gordon-Zakharov equations. The numerical results show that the proposed lifting approach is competitive with the state-of-the-art structure-preserving hyper-reduction method in terms of both accuracy and computational efficiency in the online stage while providing significant computational gains in the offline stage.

Nonlinear quantum photonics serves as a cornerstone in photonic quantum technologies, such as universal quantum computing and quantum communications. The emergence of integrated photonics platform not only offers the advantage of large-scale manufacturing but also provides a variety of engineering methods. Given the complexity of integrated photonics engineering, a comprehensive simulation framework is essential to fully harness the potential of the platform. In this context, we introduce a nonlinear quantum photonics simulation framework which can accurately model a variety of features such as adiabatic waveguide, material anisotropy, linear optics components, photon losses, and detectors. Furthermore, utilizing the framework, we have developed a device scheme, chip-scale temporal walk-off compensation, that is useful for various quantum information processing tasks. Applying the simulation framework, we show that the proposed device scheme can enhance the squeezing parameter of photon-pair sources and the conversion efficiency of quantum frequency converters without relying on higher pump power.

In this paper, we propose an alternating numerical scheme for constructing quasi-periodic solutions to a class of nonlinear partial differential equations (PDEs) with bounded perturbations, including the one-dimensional nonlinear Schrödinger (NLS) equations and nonlinear wave (NLW) equations under periodic and Dirichlet boundary conditions. A key observation concerning the resonant Q-equations allows us to establish directly a local diffeomorphism between the amplitudes and the drifted frequencies. This renders the proof considerably cleaner, since it avoids the Birkhoff normal form and the associated coordinate transformations required in classical KAM theory for PDEs.Unlike in the finite-dimensional setting, the lattice boxes must also include the spatial index, so that the multiscale induction has to be carried out in one additional dimension. This introduces two difficulties. First, the measure estimate for the excluded set of ``bad'' frequencies must account for the spatial index. For both the NLS and NLW equations, the linear frequencies and their differences are integers or close to integers; this allows the spatial dependence to be controlled through the modulus of the temporal index, so that the excluded measure remains under control. Second, a singular set may contain sites with the same temporal index but widely separated spatial indices, which obstructs the ``inversion implies localization'' process. For the one-dimensional NLS and NLW equations, however, such sites occur only in pairs with opposite spatial indices. They can therefore be separated by small boxes, after which the global inverse is obtained from the local inverses via the resolvent identity. Numerical experiments illustrate the scheme for nonlinear traveling and standing waves, exhibiting both the computed quasi-periodic solutions and the convergence of the iteration.

We study the pseudospectrum of the Kerr black hole for gravitational perturbations with spin weight s=2, the case of greatest interest in gravitational-wave astronomy. In the hyperboloidal framework with two-dimensional Chebyshev collocation, we formulate the quasinormal mode problem as a non-self-adjoint eigenvalue problem. For sneq0 the fields Ψ^{(s)} and Ψ^{(-s)} are independent, so the conserved current method yields no single-field energy norm. We overcome this with the Teukolsky--Starobinsky identities, which relate Ψ^{(-2)} to a fourth-order operator on Ψ^{(2)} and yield an H^2 energy norm after symmetrization. With the H^1 norm known for s=0, this suggests the pattern H^{|s|}, verified for s=0 and s=2. All results use an ω-independent two-field hierarchy. We find that the pseudospectrum tightens by 1.1 to 3.5 decades at each step of L^2to H^1to H^2, yet stays large in every norm. The s=+2 and s=-2 operators are isospectral but not isopseudospectral: at twelve of fourteen probes the ψ_0 resolvent exceeds the ψ_4 one by 0.19 to 0.82 decades in the H^2 norm, while at the two probes furthest along the QNM line the ordering reverses by 0.18 to 0.19 decades. The gravitational pseudospectrum exceeds the scalar one by 0.5 to 5.2 decades in the window minimum and by 5.9 decades in L^2 at ωM=0.47-0.17,i, while along the damping direction the s=2 resolvent is non-monotonic and the s=0 resolvent smooth. QNM spectral instability is therefore a universal feature of Kerr, and is stronger for gravitational perturbations.

In this work, we study the black hole light echoes in terms of the two-photon autocorrelation and explore their connection with the quasinormal modes. It is shown that the above time-domain phenomenon can be analyzed by utilizing the well-known frequency-domain relations between the quasinormal modes and characteristic parameters of null geodesics. We found that the time-domain correlator, obtained by the inverse Fourier transform, naturally acquires the echo feature, which can be attributed to a collective effect of the asymptotic poles through a weighted summation of the squared modulus of the relevant Green's functions. Specifically, the contour integral leads to a summation taking over both the overtone index and angular momentum. Moreover, the dominant contributions to the light echoes are from those in the eikonal limit, consistent with the existing findings using the geometric-optics arguments. For the Schwarzschild black holes, we demonstrate the results numerically by considering a transient spherical light source. Also, for the Kerr spacetimes, we point out a potential difference between the resulting light echoes using the geometric-optics approach and those obtained by the black hole perturbation theory. Possible astrophysical implications of the present study are addressed.

In this paper, we study the long time dynamics of small perturbations of static domain walls in weighted Sobolev spaces for the one dimensional Schrödinger map with constant Dzyaloshinskii-Moriya interaction. The perturbation equation contains derivative nonlinearities, and its linearized operator has a threshold resonance. The results are twofold. (i) We prove the asymptotic stability of the domain wall modulo the translation and rotation symmetries. More precisely, the corresponding modulation parameters converge as time tends to infinity, while the radiation decays at the sharp rate t^{-1/2}. (ii) We prove that the radiation exhibits modified scattering, with an explicit logarithmic phase correction generated by the long range cubic interaction. The proof develops geometric reduction to overcome the loss of derivatives and exploits structural cancellations in the nonlinear interactions.

External potentials break the translational invariance of nonlinear Schrödinger (NLS) equations and generally convert a continuous family of standing wave solutions into isolated pinned states. We study this mechanism for the prototypical case of a kink in the NLS equation with competing focusing cubic and defocusing quintic nonlinearities. The Lyapunov--Schmidt reduction method is used to prove that the location s_0 of the pinned kinks is selected near roots of an effective potential V_{rm eff}(s). We then determine how the translational zero eigenvalue of the Jacobian operator splits under the perturbation and prove that the sign of V_{rm eff}'(s_0) distinguishes eigendirections of positive and negative energy. We further show that if the Jacobian operator admits a negative eigenvalue, then the stability problem contains a real unstable eigenvalue. The derivation of the asymptotic expansion for the unstable eigenvalue is nonstandard because the zero eigenvalue is embedded in the continuous spectrum of the linearized operator. Finally, we show that the persistence of kinks lacks parity symmetry even if the external potential is odd. Numerical continuation, spectral computations with domains adapted to the slowly decaying eigenfunctions, and direct dynamical simulations of the time evolution corroborate the analytical predictions for different representative examples.

We investigate soliton formation and interactions in the non-integrable Gardner-Ostrovsky equation (alias the rotation-modified Gardner equation) with anomalous (positive) dispersion. This equation is relevant to the description of wave dynamics in plasmas and other dispersive media. We show that a special class of solitons, characterized by zero total mass and non-monotonic asymptotics, can emerge from pulse-like initial perturbations. Depending on the initial conditions, these solitons may form regular amplitude-ordered trains, irregular nonstationary ensembles of interacting localized structures, or stationary propagating multi-soliton complexes. We further demonstrate that soliton interactions in the Gardner-Ostrovsky equation are inherently inelastic, leading to the emergence of a dominant "soliton-champion" in closed systems. For example, under periodic boundary conditions, only the largest-amplitude soliton ultimately survives, while all smaller solitons are gradually eliminated through successive interactions. Despite their inelastic interactions, Gardner-Ostrovsky solitons exhibit remarkable robustness.

In heterogeneous networks of coupled oscillators, phase frustration typically prevents the emergence of synchronization in the Sakaguchi--Kuramoto (SK) model. In this study, we propose an analytical framework to overcome this barrier and induce complete synchronization at a specified small coupling value in oscillators governed by phase-frustrated bi-harmonic coupling. We derive an optimal set of natural frequencies that is robust against added noise and correlated with the network degree heterogeneity, along with the parameters involved in the bi-harmonic coupling function that lead to complete synchronization (r = 1). In addition, we find complete synchronization transitions accompanied by hysteresis in scale-free networks, indicating a first-order (discontinuous) phase transition, whereas Erdős--Rényi networks exhibit complete synchronization through a second-order (continuous) phase transition. Furthermore, we use the mean-field approximation in the presence of optimal frequencies to determine the critical coupling strength associated with the synchronization transition in the pure second-harmonic Sakaguchi--Kuramoto model. Here, the obtained optimal natural frequencies scale linearly with the node degree, and the critical coupling strength for the onset of synchronization is derived analytically from the self-consistent equations. In this specific regime, we observe a perfectly ordered two-cluster synchronized state. These findings remain robust for higher-order harmonic coupling schemes, as well as across a diverse range of synthetic and empirical networks, including scale-free, Erdős--Rényi, Zachary Karate Club, and the C.~elegans neural network, demonstrating their general applicability.

We establish a charge-regular formulation of separated Kerr--Newman perturbations and an explicit map from master solutions to physical radiative fields. We derive regular angular and radial first-order systems and their second-order reductions, with finite-charge deformations of the spin pm1 and pm2 Teukolsky equations. The field and boundary normalizations recover the standard Kerr conventions while accounting for the nonuniform zero-charge limit at infinity. For physical Einstein--Maxwell perturbations with the usual peeling behavior, we obtain explicit outgoing gravitational and electromagnetic amplitudes and energy fluxes at nonzero real frequency. The resulting finite-charge radiation-composition ratios depend only on the regular angular functions, independently of the radial excitation.

We study the parameter dependence and transversality properties of trajectories of the controlled ODE $ U_x = P, qquad P_x = - f(U) - βP + tilde α(x)U, arising from traveling-wave solutions of a bistable reaction-diffusion equation with control. Optimal profiles minimizing the L^1-norm of the control \tilde α are determined by the unstable and stable manifolds Γ_u, Γ_s, the critical curve P^*(U) = Uf(U), and the associated function F(U) = dP^*{dU} + f(U){P^*(U)}. We establish generic transversality properties for these objects with respect to perturbations of the speed β and the nonlinear source f, together with quantitative estimates on the first- and second-order dependence of the invariant manifolds on these parameters. We also analyze the loss of regularity at the critical speed β^{**}, where the unstable manifold approaches the strongly stable manifold of the equilibrium (U^*,0)$. These results provide the ODE ingredients used in the analysis of the structure and regularity of optimal profiles in paper [S. Bianchini and C. Trifone. Traveling profiles and control cost for a PDE describing the evolution of invasive species. 2026. arXiv: 2606.23979 [math.OC]].

Integrated circuits are a cornerstone of modern information technology, and analog wave-based architectures could enable fast and efficient processing beyond conventional charge electronics. In magnonics, spin waves provide a highly tunable, compact and energy-efficient medium for on-chip microwave signal transport and processing. However, progress has been limited to isolated elements or short devices, severely limiting the overall functional complexity and scalability. Here we realize the key elements of universal magnonic circuitry, using a single-step direct laser writing process in yttrium iron garnet, and monolithically cascade them in multi-stage programmable devices and networks. Using magneto-optical Kerr effect microscopy, we show efficient spin-wave propagation and preserved phase coherence in waveguide structures for hundreds of wavelengths. In coupled waveguides, we observe complete and periodic power transfer over several coupling lengths, and in phase shifters we achieve arbitrary, tunable phase delays. By cascading these elements, we realize programmable splitters, frequency demultiplexers, and phase-controlled 2x2 routers, where output power and relative phase can be programmed on demand via external fields. Finally, we realize programmable magnonic interferometric meshes for on-chip radio-frequency signal routing, with up to six magnonic inputs and outputs and seven cascaded stages, without the need for intermediate amplification. These direct-write cascaded networks bridge a long-standing gap in magnonic scalability, offering a viable pathway toward integrated, large-scale architectures for both classical and quantum processing.

In this paper we construct the canonical harmonic coordinates of the Kerr metric within the multipolar post-Minkowskian (MPM) formalism to the fourth post-Minkowskian (4PM) order. Based on the well known Geroch--Hansen moments of Kerr metric and Gürsel's theorem, we derive the exact canonical MPM moments M_L,S_L, which are free of any gauge moments. With these moments, we iteratively compute the gothic metric perturbation h^{μν}_{can} up to 4PM order and compute the 4PM canonical metric g_{μν}^{can}. The resulting spatial and time components of these metrics are even functions of the spin parameter a while the mixed components are odd. This parity property distinguishes the canonical coordinates from other harmonic coordinates. To contrast this minimal-gauge construction, we also extract the 1PM source moments of the Kerr metric in the Jiang--Lin coordinates. We find that the Jiang--Lin representation possesses non-vanishing gauge moments starting from the 1PM order, whereas in the canonical representation gauge moments vanish to all orders. This comparison highlights the canonical coordinates as the most gauge-pure representation of the Kerr metric in the MPM framework. The complete canonical metric for the Schwarzschild case is also computed to all PM orders. A recent independent construction by Damgaard et al. using momentum-space recursion yields 4PM equivalent results expressed as a power series in a, providing a cross-validation of our closed-form 4PM canonical metric. The coordinate transformation linking the canonical Kerr coordinates to previously known harmonic Kerr coordinates remains an open problem.

We compute Kerr-Newman quasinormal modes using a recently found exact separation of the gravitoelectric perturbation equations. For each spin-label ς=pm1, a matrix angular ordinary differential equation and a scalar second-order radial ordinary differential equation define a joint spectral problem for the complex frequency ω and separation constant λ. We solve this problem by imposing regularity at the angular poles, ingoing behavior at the event horizon, and outgoing behavior at infinity. We benchmark the numerical code built to solve the separated equations, and the resulting frequencies, against recently published spectral calculations of the coupled system. Comparisons with those results yield absolute differences of order 10^{-10} to 10^{-5}, depending on the BH parameters and overtone number. We also find numerical hints of spin-label isospectrality in both the electromagnetic-led and gravitational-led sectors of fundamental quasinormal modes, even at near-extremal Kerr-Newman configurations. These results provide numerical evidence that the separated equations reproduce Kerr-Newman quasinormal frequencies and offer a practical route to exploring the ringdown of rotating, charged black holes.

We put forward the dynamical study of a novel higher-order small network of Chialvo neurons arranged in a ring-star topology, with the neurons interacting via linear diffusive couplings. This model is perceived to imitate the nonlinear dynamical properties exhibited by a realistic nervous system where the neurons transfer information through higher-order multi-body interactions. We first analyze our model using the tools from nonlinear dynamics literature: fixed point analysis, Jacobian matrix, and bifurcation patterns. We observe the coexistence of chaotic attractors, and also an intriguing route to chaos starting from a fixed point, to period-doubling, to cyclic quasiperiodic closed invariant curves, to ultimately chaos. We numerically observe the existence of codimension-1 bifurcation patterns: saddle-node, period-doubling, and Neimark Sacker. We also qualitatively study the typical phase portraits of the system and numerically quantify chaos and complexity using the 0-1 test and sample entropy measure respectively. Finally, we study the collective behavior of the neurons in terms of two synchronization measures: the cross-correlation coefficient, and the Kuramoto order parameter.

Spacetime singularities displayed by classical black hole solutions are expected to be cured by high-energy effects, beyond the regime of validity of General Relativity. On the other hand, there are well-known examples of classical theories allowing for nonsingular black hole solutions. The most prominent is obtained by complementing the gravitational sector of General Relativity with a minimally coupled nonlinear-electrodynamics sector. It has recently been shown that purely electric/purely magnetic nonsingular black holes in an Einstein-nonlinear-electrodynamics setup are always plagued by a gradient instability. In this work, we derive the quadratic action for linear perturbations of static, spherically symmetric dyonic solutions of Einstein-nonlinear-electrodynamics theories with a general dependence on both invariants. We show that regularity of the center, absence of ghosts and angular gradient stability cannot hold simultaneously: arbitrarily close to a regular center, at least one photon polarization has a negative squared angular propagation speed. We further show that regularity drives one electromagnetic kinetic eigenvalue to zero at the center, which may limit perturbative control near the core. Evading the obstruction requires extending the theory, for example by introducing additional degrees of freedom.

We study Hamiltonian elliptic systems with prescribed bilinear mass int_{R^N}uv=a>0. We establish a Gagliardo--Nirenberg inequality in the crossed gradient pairing and bilinear mass, on scaling-invariant component-bounded classes. It identifies the critical curve 1/p+1/q=N/(N+2) and the restricted energy trichotomy. For power nonlinearities, we establish uniqueness up to common translations and nondegeneracy of positive profiles throughout the Sobolev-subcritical hyperbola. Exact scaling then classifies positive normalised solutions and identifies the unique critical mass. In dimension two, we develop a bilinear exponential Gagliardo--Nirenberg estimate with a sharp gradient threshold and a truncated scalar refinement with the optimal quartic leading coefficient. Adapting variational ideas from [Cassani-Tarsi, Calc.Var.PDE (2015)] we combine a mass-normalising quotient, reduction over the full negative fibres and compactness below the concentration threshold to obtain least-energy positive radial solutions for pure exponential nonlinearities at every prescribed mass below the cubic limiting mass. Local perturbative branches and a small-frequency exponential branch yield explicit mass-response formulas.

We report an optical method of generating arbitrary polarization states by manipulating the thicknesses of a pair of uniaxial birefringent plates, the optical axes of which are set at a crossing angle of {\pi}/4. The method has the remarkable feature of being able to generate a distribution of arbitrary polarization states in a group of highly discrete spectra without spatially separating the individual spectral components. The target polarization-state distribution is obtained as an optimal solution through an exploration. Within a realistic exploration range, a sufficient number of near-optimal solutions are found. This property is also reproduced well by a concise model based on a distribution of exploration points on a Poincar\'e sphere, showing that the number of near-optimal solutions behaves according to a power law with respect to the number of spectral components of concern. As a typical example of an application, by applying this method to a set of phase-locked highly discrete spectra, we numerically demonstrate the continuous generation of a vector-like optical electric field waveform, the helicity of which is alternated within a single optical cycle in the time domain.

Tellegen medium has long been a topic of debate, with its existence being contested over several decades. It was first proposed by Tellegen in 1948 and is characterized by a real-valued cross coupling between electric and magnetic responses, distinguishing it from the well-known chiral medium that has imaginary coupling coefficients. Significantly, Tellegen responses are closely linked to axion dynamics, an extensively studied subject in condensed matter physics. Here, we report the realization of Tellegen metamaterials in the microwave region through a judicious combination of subwavelength metallic resonators, gyromagnetic materials, and permanent magnet discs. We observe the key signature of the Tellegen response, i.e. a Kerr rotation for reflected wave, while the polarization remains the same in the transmission direction. The retrieved effective Tellegen parameter is several orders of magnitude greater than that of natural materials. Our work opens door to a variety of nonreciprocal photonic devices and may provide a platform for studying axion physics.

Synchronization in one dimension displays generic scale invariance with universal properties previously observed in surface kinetic roughening and the wider context of the Kardar-Parisi-Zhang (KPZ) universality class. This has been established for phase oscillators and also for some limit-cycle oscillators, both in the presence of columnar (quenched) disorder and of time-dependent noise, by extensive numerical simulations, and has been analytically motivated by continuum approximations in the strong oscillator coupling limit. The robustness and the precise boundaries in parameter space for such critical behavior remain unclear, however, which may preclude further developments, including the extension of these results to higher dimensions and the experimental observation of nonequilibrium criticality in synchronizing (e.g.~electronic or chemical) oscillators. We here present complete numerical phase diagrams of one-dimensional synchronization, including saturation times and values, but, most importantly, also dynamical features giving insight into the gradual emergence of synchronous dynamics, based on systems of phase oscillators with either type of randomness. In the absence of synchronization, the dynamics evolves as expected for random deposition (for time-dependent noise) or linear growth (for columnar disorder), while a crossover from Edwards-Wilkinson to Kardar-Parisi-Zhang behavior (with the corresponding type of randomness) is observed as the randomness strength, or the nonoddity of the coupling among oscillators, is increased in the synchronous region -- their combined effect being partially captured by the so-called KPZ coupling. The distortion of scaling due to phase slips near the desynchronization boundary, a feature that is likely to play a role in experimental contexts, is also discussed.

Vacuum Kerr perturbations in general relativity have identical even- and odd-parity quasinormal frequencies. We establish this parity isospectrality for linear gravitoelectromagnetic perturbations of subextremal Kerr--Newman--de Sitter black holes, without a slow-rotation or small-charge expansion. We reconstruct the radiative metric and gauge-potential perturbations directly from gauge-invariant master variables in radiation gauge, without an intermediate complex potential.

We propose a novel nonlinear bidirectionally coupled heterogeneous chain network whose dynamics evolve in discrete time. The backbone of the model is a pair of popular map-based neuron models, the Chialvo and the Rulkov maps. This model is assumed to proximate the intricate dynamical properties of neurons in the widely complex nervous system. The model is first realized via various nonlinear analysis techniques: fixed point analysis, phase portraits, Jacobian matrix, and bifurcation diagrams. We observe the coexistence of chaotic and period-4 attractors. Various codimension-1 and -2 patterns for example saddle-node, period-doubling, Neimark-Sacker, double Neimark-Sacker, flip- and fold-Neimark Sacker, and 1:1 and 1:2 resonance are also explored. Furthermore, the study employs two synchronization measures to quantify how the oscillators in the network behave in tandem with each other over a long number of iterations. Finally, a time series analysis of the model is performed to investigate its complexity in terms of sample entropy.

This paper derives the second-order positive Burgers' equation from the standard Burgers' hierarchy to explore its complete integrability and exact analytical solutions. We construct this higher-order nonlinear evolution equation by systematically applying the recursion operator to the classical Burgers' equation. Expanding on this structural framework, we then derive the explicit third-order equation and use Complete Bell Polynomials to generalize the n-th order hierarchy. Through the Cole-Hopf transformation, the second-order nonlinear equation rigorously maps to the linear third-order dispersion equation. We establish complete integrability by explicitly formulating the scalar Lax pair (zero-curvature representation), which allows us to directly derive the associated differential and algebraic Darboux transformations. To systematically classify explicit stationary, time-dependent traveling wave, and self-similar profiles, we apply several techniques to the linear domain: separation of variables, the Hirota perturbation method, traveling wave reduction via the Complete Discrimination System for Polynomial Method (CDSPM), and Lie similarity reduction. Crucially, our analysis demonstrates the exact finite truncation of the Hirota perturbation series. We conclude by outlining how this equation impacts the theoretical understanding of fluid dynamics, nonlinear transport phenomena, and higher-order wave propagation.

Gravitational-wave approximants are essential for gravitational-wave astronomy, allowing the coverage binary black hole parameter space for inference or match filtering without costly numerical relativity (NR) simulations, but generally trading some accuracy for computational efficiency. To reduce this trade-off, NR surrogate models can be constructed using interpolation within NR waveform space. We present a 2-stage training approach for neural network-based NR surrogate models. Initially trained on approximant-generated waveforms and then fine-tuned with NR data, these dual-stage artificial neural surrogate (DANSur) models offer rapid and competitively accurate waveform generation, generating millions in under 20ms on a GPU while keeping mean mismatches with NR around 10^{-4}. Implemented in the bilby framework, we show they can be used for parameter estimation tasks.

The Korteweg-de Vries (KdV) equation serves as a foundational model in nonlinear wave physics, describing the balance between dispersive spreading and nonlinear steepening that gives rise to solitons. This article introduces sangkuriang, an open-source Python library for solving this equation using Fourier pseudo-spectral spatial discretization coupled with adaptive high-order time integration. The implementation leverages just-in-time (JIT) compilation for computational efficiency while maintaining accessibility for instructional purposes. Validation encompasses progressively complex scenarios including isolated soliton propagation, symmetric two-wave configurations, overtaking collisions between waves of differing amplitudes, and three-body interactions. Conservation of the classical invariants is monitored throughout, with deviations remaining small across all test cases. Measured soliton velocities conform closely to theoretical predictions based on the amplitude-velocity relationship characteristic of integrable systems. Complementary diagnostics drawn from information theory and recurrence analysis confirm that computed solutions preserve the regular phase-space structure expected for completely integrable dynamics. The solver outputs data in standard scientific formats compatible with common analysis tools and generates visualizations of spatiotemporal wave evolution. By combining numerical accuracy with practical accessibility on modest computational resources, sangkuriang offers a platform suitable for both classroom demonstrations of nonlinear wave phenomena and exploratory research into soliton dynamics.

Optical resonances in nanostructures enable strong enhancement of nonlinear processes at the nanoscale, such as second-harmonic generation (SHG), with high-Q modes providing intensified light--matter interactions and sharp spectral selectivity for applications in filtering, sensing, and nonlinear spectroscopy. Thanks to the recent advances in thin-film lithium niobate (TFLN) technology, these key features can be now translated to lithium niobate for realizing novel nanoscale nonlinear optical platforms. Here, we demonstrate a large-area metasurface, realized by scalable nanoimprint lithography, comprising a slanted titanium dioxide (TiO_2) nanograting on etchless TFLN for efficient narrowband SHG. This is enabled by the optimal coupling of quasi-bound state in the continuum (q-BIC) modes with a narrowband pulsed laser pump. The demonstrated normalized SHG efficiency is 0.15%,cm^2/GW, which is among the largest reported for LN metasurfaces. The low pump peak intensity (3.64~kW/cm^2) employed, which enables SHG even by continuous-wave pumping, allows envisioning integrated and portable photonic applications. SHG wavelength tuning from 870 to 920~nm with stable output power as well as polarization control is also achieved by off-normal pump illumination. This versatile platform opens new opportunities for sensing, THz generation and detection, and ultrafast electro-optic modulation of nonlinear optical signals.

Materials that undergo internal transformations are usually described in solid mechanics by multi-well energy functions that account for both elastic and transformational behavior. In order to separate the two effects, physicists use instead phase-field-type theories where conventional linear elastic strain is quadratically coupled to an additional field that describes the evolution of the reference state and solely accounts for nonlinearity. In this paper we propose a systematic method allowing one to split the non-convex energy into harmonic and nonharmonic parts and to convert a nonconvex mechanical problem into a partially linearized phase-field problem. The main ideas are illustrated using the simplest framework of the Peierls-Nabarro dislocation model.

We study spontaneous scalarization of static, spherically symmetric black holes in scalar--Gauss--Bonnet gravity with a Ricci coupling F=1 βϕ^{2}/4+γβ^{2}ϕ^{4}+O(ϕ^{6}) that nonlinearly completes the quadratic one. For arbitrary couplings and potential, we derive the near-horizon regularity condition and horizon curvature invariants in closed form; scalarized branches terminate where this condition degenerates, at finite horizon curvature. A weakly nonlinear expansion fixes the bifurcation direction exactly: for a massless scalar, its governing coefficient is quadratic in β, changes sign at β=1.1156, and depends linearly on a quartic self-interaction. At equal horizon values of the scalar, completions differ in mass, to leading order, in proportion to γ. A radial-perturbation master equation for arbitrary couplings confirms the exchange of stability at the bifurcation and turning points. Consequently, the domain of radially stable black holes shrinks as γ increases over the range studied; it is smaller for the exponential completion than for the quadratic truncation.

Motivated by searches for weak primordial non-Gaussianity in the cosmic microwave background, we investigate perturbative departures from Gaussian stochastic gravitational wave background statistics using pulsar timing arrays. We consider a quadratic ansatz that shows three-point correlations at first order in the nonlinear coupling and covariance corrections at second order. We first examine the ansatz for gravitational wave helicity amplitudes. However, the timing residual bispectrum that this produces is not manifestly invariant under local polarization basis rotations for tensor and vector modes. Then, we formulate a polarization-frame-invariant phenomenological model for detector-projected amplitudes and evaluate its one-pulsar timing residual third moment with a simplified response. Our numerical benchmarks have shown that this gives a very small Gaussian-rms-normalized skewness.

We study how a radially oscillating thin shell outside a black hole (BH) affects gravitational wave ringdown and derive matching conditions for polar and axial perturbations from the linearized Israel junction conditions on the moving worldtube. Periodic shell motion produces Floquet sidebands in the scattered wave. For a distant shell, the motion has little effect on the prompt ringdown and only weakly modifies the late time echoes. When the shell is closer to the BH, a replica of a long lived shell mode enters the incident frequency band, increasing the late time echo amplitude by roughly two orders of magnitude. We also identify an exceptional point where two polar modes coalesce and find the contribution of its second order pole in the late time waveform.

The two-body problem of variational electrodynamics possesses differential-delay equations of motion with state-dependent delays of neutral type and solutions that can have velocity discontinuities on countable sets. From a periodic orbit possessing some mild properties at breaking points, we define a synchronization function in R x R3, which is further used to construct two bounded oscillatory functions vanishing at breaking points and whose first derivatives are continuous and defined everywhere but at breaking points. The oscillatory functions are associated with a PDE identity in H2(R3), and we postulate ordering conditions for the PDE identity to define a Fredholm-Schroedinger operator with an O(1/r2) spin-orbit forcing term belonging to L2(R3). As an application, we introduce the Chemical Principle criterion to select orbits with asymptotically vanishing far-fields and estimate the Bohr radius parameter of the Fredholm-Schroedinger PDE using the boundary-layer of orbits chosen according to the Chemical Principle criterion. Last, working backward, we derive a Chemical Principle-like condition from the ordering conditions.

Generation of high-fidelity amplified pulse bursts with a regular interpulse interval yields, in the spectral domain, an equidistant pattern of narrowband spectral modes, similar to frequency combs produced by cw mode-locked lasers, but with greatly increased pulse energy. Despite their great potential for nonlinear spectroscopy, material processing, etc., such long frequency-stable bursts are difficult to generate and amplify because of prominent temporal intensity modulation even after strong dispersive pulse stretching. This study presents a burst generation method based on a master-oscillator regenerative-amplifier system that allows for chirped-pulse amplification (CPA) with high scalability in pulse number. A gradual smoothing of temporal intensity profiles at an increasing number of pulses is discovered, demonstrating an unexpected recovery of the CPA performance at terahertz (THz) intraburst repetition rates. In consequence, a self-referenced stable burst spectral peak structure with megahertz (MHz) peak width is generated, without risk of amplifier damage caused by interference of chirped pulses. This result eliminates limitations in burst amplification and paves the way for advancements in ultrashort-pulse burst technology, particularly for its use in nonlinear optical applications.

We present a new derivation of the exact compact oscillon in the signum-Gordon model using Fourier methods. This approach decomposes the oscillon into an infinite, uniformly convergent series of discrete modes consisting of a fundamental frequency and its odd higher harmonics, in contrast to standard analytic potentials, where the corresponding infinite perturbative series fails to converge. Crucially, our oscillon evades the non-existence theorem for spatially localized, small-amplitude periodic states. We investigate the accuracy of truncating the Fourier series and find that the primary mode alone provides a remarkably accurate approximation of the exact solution, with agreement improving significantly when the first two non-vanishing harmonic modes are included. Furthermore, we generalize this framework to a swaying compact oscillon with a periodically moving boundary. We show that describing such an oscillon requires even-order modes, whose coupling with the odd source terms induces a dynamic modulation that generates the swaying motion, even though the spatial Fourier profiles themselves are time-independent.

We model and study the processes of excitation, absorption, and transfer in various networks. The model consists of a harmonic oscillator representing a single-mode radiation field, a qubit acting as an antenna, a network through which the excitation propagates, and a qubit at the end serving as a sink. We investigate how off-resonant excitations can be optimally absorbed and transmitted through the network. Three strategies are considered: optimising network energies, adjusting the couplings between the radiation field, the antenna, and the network, or introducing and optimising driving fields at the start and end of the network. These strategies are tested on three different types of network with increasing complexity: nearest-neighbour and star configurations, and one associated with the Fenna-Matthews-Olson complex. The results show that, among the various strategies, the introduction of driving fields is the most effective, leading to a significant increase in the probability of reaching the sink in a given time. This result remains stable across networks of varying dimensionalities and types, and the driving process requires only a few parameters to be effective.

Exact firing rate models, also known as next-generation neural mass models (NG-NMMs), provide a rigorous description of the dynamics of neural populations. While in its simplest form a single population only displays fixed-point activity, multi-population models may display a range of different behaviors. In this work, we study the dynamics of all-excitatory or all-inhibitory NG-NMMs coupled through sparse random networks with row-normalized network topology. Linear stability analysis of the homogeneous states of the system, representing asynchronous neural activity, provides a dispersion relation linking the emergence of spatiotemporal dynamics to the spectra of the connectivity matrix. Using bounds from random matrix theory, we identify the parameter regions where instabilities occur. In undirected networks, only inhibitory systems produce heterogeneous stationary patterns, corresponding to a winner-takes-all mechanism. In directed networks, exotic rhythmic states with high frequencies emerge in both, excitatory and inhibitory systems. Numerical simulations reveal that these hectic oscillatory states correspond to high-dimensional chaos with extensive properties.

This paper concerns the planar Liénard system \(\dot x=y-F(x),\ \dot y=-x\), where \(F(x)\) is a continuous piecewise linear function with exactly \(n\) fold points. Tonnelier [SIAM J. Appl. Math. 63 (2002)] conjectured that the maximum number of limit cycles of the system is \(n\) when \(F\) has exactly \(n\) fold points. The conjecture was confirmed for \(n=1\) and \(n=2\) in [J. Nonlinear Sci. 25 (2015)] and [J. Lond. Math. Soc. 113 (2026)], respectively, whereas the case \(n\ge3\) remained open. In this paper, we show that the maximal number of limit cycles is at least \(|3n-4|\) for \(n\in\mathbb N^+\), thereby disproving Tonnelier's conjecture for \(n\ge3\). The proof reveals a unified multiscale perturbation mechanism underlying the creation and coexistence of multiple limit cycles. Moreover, we prove that the number of limit cycles admits the finite upper bound \(2^{28(n+1)^2}\).

Chip-integrated nonlinear photonics holds the key for advanced optical information processing with superior performance and novel functionalities. Here, we present an optimally mode-matched, periodically poled lithium niobate nanowaveguide for efficient parametric frequency conversions on chip. Using a 4-mm nanowaveguide with subwavelength mode confinement, we demonstrate second harmonic generation with efficiency over 2200%~W^{-1}cm^{-2}, and broadband difference frequency generation with similar efficiency over a 4.5-THz spectral span. These allow us to generate correlated photon pairs over multiple frequency channels via spontaneous parametric down conversion, all in their fundamental spatial modes, with a coincidence to accidental ratio as high as 600. The high efficiency and dense integrability of the present chip devices may pave a viable route to scalable nonlinear applications in both classical and quantum domains.

This study introduces amangkurat, an open-source Python library designed for the robust numerical simulation of relativistic scalar field dynamics governed by the nonlinear Klein-Gordon equation in (1+1)D spacetime. The software implements a hybrid computational strategy that couples Fourier pseudo-spectral spatial discretization with a symplectic Størmer-Verlet temporal integrator, ensuring both exponential spatial convergence for smooth solutions and long-term preservation of Hamiltonian structure. To optimize performance, the solver incorporates adaptive timestepping based on Courant-Friedrichs-Lewy (CFL) stability criteria and utilizes Just-In-Time (JIT) compilation for parallelized force computation. The library's capabilities are validated across four canonical physical regimes: dispersive linear wave propagation, static topological kink preservation in phi-fourth theory, integrable breather dynamics in the sine-Gordon model, and non-integrable kink-antikink collisions. Beyond standard numerical validation, this work establishes a multi-faceted analysis framework employing information-theoretic entropy metrics (Shannon, Rényi, and Tsallis), kernel density estimation, and phase space reconstruction to quantify the distinct phenomenological signatures of these regimes. Statistical hypothesis testing confirms that these scenarios represent statistically distinguishable dynamical populations. Benchmarks on standard workstation hardware demonstrate that the implementation achieves high computational efficiency, making it a viable platform for exploratory research and education in nonlinear field theory.

We present a spacetime that serves as a horizonless mimicker of extremal black holes. Unlike previously studied mimickers of black holes with non-degenerate horizons, whose geometries are of the wormhole type and consist of two asymptotically flat regions connected by a very long throat, the mimicker of an extremal black hole possesses a single asymptotically flat region at one end and an infinitely long throat at the other. In the throat region, the spacetime approaches the direct-product geometry M_{1,1} times S^2, where M_{1,1} is two-dimensional Minkowski spacetime and S^2 is the two-sphere. We investigate scalar-field dynamics and the fate of the Aretakis instability. Although Aretakis-like modes arise in a local analysis of the throat, they do not lead to a physical instability of the mimicker. A scalar perturbation initially localized in the throat gives rise, at late times, to a sequence of signals with a characteristic separation t_{rm delay}sim 1/λ, where λll 1 is a deformation parameter. This timescale is parametrically larger than the echo time t_{rm echo}sim ln(1/λ) characteristic of non-extremal black-hole mimickers. We refer to this sequence as a {\it long-delay signal train}. Geometrically, the periodicity of the long-delay signals is associated with periodic geodesics on S^2. We then extend the construction to extremal Kerr. In this case, the throat region approaches a generalized product geometry involving M_{1,1} and a two-dimensional surface Σ_2. The corresponding signals are expected to form a quasi-periodic signal train, reflecting the quasi-periodic geodesic motion on Σ_2. We also comment on the generalization to wormhole mimickers of non-extremal black holes and on the implications of these results for unitarity in the context of the AdS/CFT correspondence.

We determine the quadrupolar logarithmic tidal response of electrically charged Einstein-Euler-Heisenberg black holes from the coupled static odd-parity gravitational and electromagnetic equations. Although the second electromagnetic invariant vanishes on the electric background, its quadratic interaction contributes to the axial fluctuation equations. At first order in the Euler-Heisenberg coupling a, a direct asymptotic recursion gives the canonical running matrix C_{rm can}^{rm EH}=(9aQ^2/10)left(smallmatrix0&-Q-Q&Msmallmatrixright), defined as the coefficients multiplying the canonical source vector in the r^{-2}log(r_0/r) term. The resulting local coefficients retain the full dependence on the subextremal ratio Q{M} at this perturbative order. The two quartic invariants partially cancel in both nonzero channels, while the action-normalized fields make gravitoelectromagnetic reciprocity explicit. The local extremal limit of the running matrix reproduces the corresponding two-invariant effective-field-theory result after convention conversion. Allowing independent quartic couplings further shows that identical electric background geometries can have different axial running matrices and yields algebraic inverse relations within the specified two-operator model. The calculation determines local logarithmic running within minimally coupled quartic electrodynamics; the finite horizon-matched response requires an additional global matching calculation.

The transition of an impulsively excited kink oscillation of a solar coronal loop to an oscillation with a stationary amplitude, i.e., the damping pattern, is determined using the low-dimensional self-oscillation model. In the model, the decayless kink oscillations are sustained by the interaction of the oscillating loop with an external quasi-steady flow. The analytical solution is based on the assumption that the combined effect of the effective dissipation, for example, by resonant absorption, and interaction with an external flow, is weak. The effect is characterised by a dimensionless coupling parameter. The damping pattern is found to depend upon the initial amplitude and the coupling parameter. The approximate expression shows a good agreement with a numerical solution of the self-oscillation equation. The plausibility of the established damping pattern is demonstrated by an observational example. Notably, the damping pattern is not exponential, and the characteristic decay time is different from the time determined by the traditionally used exponential damping fit. Implications of this finding for seismology of the solar coronal plasmas are discussed. In particular, it is suggested that a very rapid, in less than the oscillation period, decay of the oscillation to the stationary level, achieved for larger values of the coupling parameter, can explain the relative rareness of the kink oscillation events.

Pulsed visible lasers either by Q-switching or mode locking have been attracting intense attentions both in solid-state laser and fiber laser. Here, we report on the simultaneous manipulation of reconfigurable sub-pulse sequences and customizable high-order vortex beams in an actively Q-switched visible laser. On the one hand, pulse sequences with up to 4 sub-pulses could be generated and fully controlled by means of an acoustic-optic modulator driven by an arbitrary waveform generator. Both pulse number and pulse intensity can be manipulated through the programmable step-signal, which is also theoretically simulated through the rate equations. On the other hand, assisted by the off-axis pumping technique and the astigmatic mode conversion, the laser cavity could emit high-quality vortex beams carrying Laguerre-Gaussian modes up to 30th order. To the best of our knowledge, this is the most flexible active manipulations not only on the intensity distribution of the transverse modes but also on the temporal distribution of the pulse sequences in a visible laser. The versatile manipulating techniques in this work could be immediately implemented into all other solid-state lasers to obtain sub-pulse vortex beams, which may provide enhanced functionality and flexibility for a large range of laser systems.

The strong coupling between magnetism and ferroelectricity was found in rare earth manganites, where the electric polarization could be induced by special magnetic ordering. There is no theoretical model that would allow us to study the static and dynamic properties of electric polarization in strongly correlated magnetic dielectrics. In the presented research, we have taken the main step towards the construction of such a fundamental model, and made a direct connection between the microscopic Katsura-Nagaosa-Balatsky theory and Mostovoy's phenomenological model for magnetically induced polarization. A novel description of the ferroelectricity of spin origin is proposed within the framework of the many-particle quantum hydrodynamics method. It is applied to the study of cells of magnetic ions, where the electric dipole moment is proportional to the vector product of spins. Our approach is based on the many-particle Pauli equation, where the influence of an external magnetic field is considered. We define the electric dipole moment operator of the ion cell and introduce the macroscopic polarization as the quantum mechanical average of that operator. We formulate a model for the description of nonequilibrium polarization and derive a new polarization evolution equation. The polarization switching in ferroelectric magnets with the spiral spin-density-wave state is considered, and we demonstrate that the proposed model yields known results and can predict novel effects. The dynamic magnetoelectric effect can be investigated by employing this novel equation to study the evolution of polarization.

In this work, we consider the generalized Benjamin-Bona-Mahony equation $partial_t u+partial_x u+partial_x( |u|^pu)-partial_t partial_x^{2}u=0, quad(t,x) in R times R, with p>4. This equation has the traveling wave solutions \phi_{c}(x-ct), for any frequency c>1. It has been proved by Souganidis and Strauss Strauss-1990 that, there exists a number c_{0}(p)>1, such that solitary waves \phi_{c}(x-ct) with 1<c<c_{0}(p) is orbitally unstable, while for c>c_{0}(p), \phi_{c}(x-ct) is orbitally stable. The linear exponential instability in the former case was further proved by Pego and Weinstein Pego-1991-eigenvalue. In this paper, we prove the orbital instability in the critical case c=c_{0}(p)$.

We propose a neural network for both forward and inverse continuous nonlinear Fourier transforms, NFT and INFT respectively. We demonstrate the network's capability to perform NFT and INFT for a random mix of NFDM-QAM signals. The network transformations (NFT and INFT) exhibit true characteristics of these transformations; they are significantly different for low and high-power input pulses. The network shows adequate accuracy with an RMSE of 5e-3 for forward and 3e-2 for inverse transforms. We further show that the trained network can be used to perform general nonlinear Fourier transforms on arbitrary pulses beyond the training pulse types.

Artificial neural networks have become a staple computing technique in many fields. Yet, they present fundamental differences with classical computing hardware in the way they process information. Photonic implementations of neural network architectures potentially offer fundamental advantages over their electronic counterparts in terms of speed, processing parallelism, scalability and energy efficiency. Scalable and high performance photonic neural networks (PNNs) have been demonstrated, yet they remain scarce. In this work, we study the performance of such a scalable, fully parallel and autonomous PNN based on a large area vertical-cavity surface-emitting laser (LA-VCSEL). We show how the performance varies with different physical parameters, namely, injection wavelength, injection power, and bias current. Furthermore, we link these physical parameters to the general computational measures of consistency and dimensionality. We present a general method of gauging dimensionality in high dimensional nonlinear systems subject to noise, which could be applied to many systems in the context of neuromorphic computing. Our work will inform future implementations of spatially multiplexed VCSEL PNNs.

We prove that all excited states -sin(nx), ngeq2, of the De Gregorio equation on the torus are nonlinearly unstable in the sense of Hadamard. More precisely, perturbations arbitrarily small in H^2 leave a fixed H^1 neighborhood of the state. For every ngeq2, the linearized operator has a real eigenvalue λ_nin(0.56,0.6). To prove this, we transform the eigenvalue problem into a Fuchsian equation on the complex disk and obtain a matching condition for the eigenvalue. This condition is verified rigorously using interval arithmetic. The nonlinear instability follows from a bootstrap argument in the spirit of Guo, Hallstrom, and Spirn.

Post-merger gravitational wave echoes provide a unique opportunity to probe the near-horizon structure of astrophysical black holes, that may be modified due to non-perturbative quantum gravity phenomena. However, since the waveform is subject to large theoretical uncertainties, it is necessary to develop model-agnostic search methods for detecting echoes from observational data. A promising strategy is to identify the characteristic quasinormal modes (QNMs) associated with echoes, {\it in frequency space}, which complements existing searches of quasiperiodic pulses in time. In this study, we build upon our previous work targeting these modes by incorporating relative phase information to optimize the Bayesian search algorithm. Using a new phase-marginalized likelihood, the performance can be significantly improved for well-resolved QNMs. This enables an efficient model-agnostic search for QNMs of different shapes by using a simple search template. To demonstrate the robustness of the search algorithm, we construct four complementary benchmarks for the echo waveform that span a diverse range of different theoretical possibilities for the near-horizon structure. We then validate our Bayesian search algorithms by injecting the benchmark models into different realizations of Gaussian noise. Using two types of phase-marginalized likelihoods, we find that the search algorithm can efficiently detect the corresponding QNMs. Therefore, our search strategy provides a concrete Bayesian and model-agnostic approach to "quantum black hole seismology".

We carried out numerical simulations of propagation of spin waves (magnons in quantum language) in a yttrium-iron garnet film. The numerical model is based on an original formalism. We demonstrated that a potential barrier for magnons, created by an Oersted field of a dc current flowing through a wire sitting on top of the film, is able to act as an electrically controlled partly transparent mirror for the magnons. We found that the mirror transparency can be set to 50% by properly adjusting the current strength, thus creating a semi-transparent mirror. A strong Hong-Ou-Mandel Effect for single magnons is expected in this configuration. The effect must be seen as two single magnons, launched simultaneously into the film from two transducers located from the opposite sides of the mirror, creating a two-microwave-photon state at the output port of one of the transducers. The probability of seeing those two-photon states at the output port of either transducer must be the same for both transducers.

In order to study oscillators coupled by pulses emitted at discrete times, it is generally assumed that the effect of each pulse is an instantaneous phase shift, with a possible conduction delay between emission and receipt. However, we are interested in neural oscillators in which each pulse (action potential) activates a biexponential synapse, and at high frequencies, the duration of the synaptic conductance may be greater than the network period. Therefore, the effect of received pulses can summate over the course of several cycles. To overcome this limitation, we previously defined a mean field approach for a single synchronous population. Here, we extend it to two alternating synchronous populations by assuming a perturbation of a single oscillator from one of the synchronous populations which is represented by a single self-connected neural oscillator. The train of delayed biexponential synapses emitted by each oscillator is divided into a tonic and a phasic component. Because of the continuous rather than pulsatile nature of the input, we had to drop the concept of oscillator phase and derive self-consistent criteria for the existence and stability of an alternating firing pattern between two synchronous populations based solely on the perturbation of time intervals from their steady state values. Simulations showed that for high frequency oscillations as defined above, the mean field approach predicts the existence and stability of phase-locking between two synchronous populations better than the instantaneous phase shift approach. This approach may generalize to other forms of coupling amongst non-neural oscillators.

Quantum reservoir computing is strongly emerging for sequential and time series data prediction in quantum machine learning. We make advancements to the quantum noise-induced reservoir, in which reservoir noise is used as a resource to generate expressive, nonlinear signals that are efficiently learned with a single linear output layer. We address the need for quantum reservoir tuning with a novel and generally applicable approach to quantum circuit parameterization, in which tunable noise models are programmed to the quantum reservoir circuit to be fully controlled for effective optimization. Our systematic approach also involves reductions in quantum reservoir circuits in the number of qubits and entanglement scheme complexity. We show that with only a single noise model and small memory capacities, excellent simulation results were obtained on nonlinear benchmarks that include the Mackey-Glass system for 100 steps ahead in the challenging chaotic regime.

We propose the Kuramoto Graph Neural Network (KuramotoGNN), a novel class of continuous-depth graph neural networks (GNNs) that employs the Kuramoto model to mitigate the over-smoothing phenomenon, in which node features in GNNs become indistinguishable as the number of layers increases. The Kuramoto model captures the synchronization behavior of non-linear coupled oscillators. Under the view of coupled oscillators, we first show the connection between Kuramoto model and basic GNN and then over-smoothing phenomenon in GNNs can be interpreted as phase synchronization in Kuramoto model. The KuramotoGNN replaces this phase synchronization with frequency synchronization to prevent the node features from converging into each other while allowing the system to reach a stable synchronized state. We experimentally verify the advantages of the KuramotoGNN over the baseline GNNs and existing methods in reducing over-smoothing on various graph deep learning benchmark tasks.

Physics-Informed Neural Networks (PINNs) have emerged as a powerful framework for solving partial differential equations (PDEs). However, standard MLP-based PINNs often fail to converge when dealing with complex initial value problems, leading to solutions that violate causality and suffer from a spectral bias towards low-frequency components. To address these issues, we introduce NeuSA (Neuro-Spectral Architectures), a novel class of PINNs inspired by classical spectral methods, designed to solve linear and nonlinear PDEs with variable coefficients. NeuSA learns a projection of the underlying PDE onto a spectral basis, leading to a finite-dimensional representation of the dynamics which is then integrated with an adapted Neural ODE (NODE). This allows us to overcome spectral bias, by leveraging the high-frequency components enabled by the spectral representation; to enforce causality, by inheriting the causal structure of NODEs, and to start training near the target solution, by means of an initialization scheme based on classical methods. We validate NeuSA on canonical benchmarks for linear and nonlinear wave equations, demonstrating strong performance as compared to other architectures, with faster convergence, improved temporal consistency and superior predictive accuracy. Code and pretrained models are available in https://github.com/arthur-bizzi/neusa.

Tobasco et al. [Physics Letters A, 382:382-386, 2018; see https://doi.org/10.1016/j.physleta.2017.12.023] recently suggested that trajectories of ODE systems that optimize the infinite-time average of a certain observable can be localized using sublevel sets of a function that arise when bounding such averages using so-called auxiliary functions. In this paper we demonstrate that this idea is viable and allows for the computation of extremal unstable periodic orbits (UPOs) for polynomial ODE systems. First, we prove that polynomial optimization is guaranteed to produce auxiliary functions that yield near-sharp bounds on time averages, which is required in order to localize the extremal orbit accurately. Second, we show that points inside the relevant sublevel sets can be computed efficiently through direct nonlinear optimization. Such points provide good initial conditions for UPO computations. As a proof of concept, we then combine these methods with a single-shooting Newton-Raphson algorithm to study extremal UPOs for a nine-dimensional model of sinusoidally forced shear flow. We discover three previously unknown families of UPOs, one of which simultaneously minimizes the mean energy dissipation rate and maximizes the mean perturbation energy relative to the laminar state for Reynolds numbers approximately between 81.24 and 125.

Photon loss and dephasing rapidly degrade the sensitivity of quantum sensors, yet systematic methods for designing error-correcting codes whose geometry is simultaneously adapted to the sensing task and the noise channel do not exist. Here we establish that orbital-angular-momentum (OAM) encoding and Gottesman-Kitaev-Preskill (GKP) lattice geometry are structurally coupled: an OAM mode of topological charge ell induces a phase-space rotation θ_ell=ellπ/ell_{max}, corresponding to a family of twisted GKP stabilizer lattices. Using an end-to-end differentiable Strawberry Fields--TensorFlow circuit, we jointly optimise ell, the lattice aspect ratio r, and the finite-energy envelope ε to maximise quantum Fisher information subject to P_{rm err}leq10^{-3}. The optimum occurs at the fractional charge ell=1.5 (θ=67.5^circ), implementable with a half-integer spiral phase plate, which reduces P_{rm err} by 23.9times relative to the square-lattice baseline while leaving F_Q unchanged to within 0.2%. This surpasses the best integer value (ell=2, 15.7times) and arises from an exact 180^circ periodicity of the P_{rm err}(θ) landscape, confirmed analytically and numerically. We derive a transcendental balance equation for the optimal angle θ^*(η,γ,r) and prove that it decreases with both γ and η. A Shannon-inspired metrological capacity C=F_Qcdot(-ln P_{rm err}), maximised at ell=1.5 with a 41% gain over the square lattice, quantifies the joint sensitivity--fault-tolerance resource. These results establish a geometric design principle for noise-adaptive quantum sensors and a fully open-source differentiable template extensible to other bosonic code families.

Fiber Fabry--Perot (FFP) resonators of a few centimeters are optimized as a function of the reflectivity of the mirrors and the dimensions of the intra-cavity waveguide. Loaded quality factor in excess of 10^9, with an optimum of 4___x___10^9, together with an intrinsic quality factor larger than 10^10 and intrinsic finesse in the range of 10^5 have been measured. An application to the stabilization of laser frequency fluctuations is presented.

We present GravLensX, an innovative method for rendering black holes with gravitational lensing effects using neural networks. The methodology involves training neural networks to fit the spacetime around black holes and then employing these trained models to generate the path of light rays affected by gravitational lensing. This enables efficient and scalable simulations of black holes with optically thin accretion disks, significantly decreasing the time required for rendering compared to traditional methods. We validate our approach through extensive rendering of multiple black hole systems with superposed Kerr metric, demonstrating its capability to produce accurate visualizations with significantly 15times reduced computational time. Our findings suggest that neural networks offer a promising alternative for rendering complex astrophysical phenomena, potentially paving a new path to astronomical visualization.

Exciton-polaritons are unique quasiparticles with hybrid properties of an exciton and a photon, opening ways to realize ultrafast strongly nonlinear systems and inversion-free lasers based on Bose-Einstein polariton condensation. However, the real-world applications of the polariton systems are still limited due to the temperature operation and costly fabrication techniques for both exciton materials and photon cavities. 2D perovskites represent one of the most prospective platforms for the realization of strong light-matter coupling since they possess room-temperature exciton states with large oscillator strength and can simultaneously provide planar photon cavities with high field localization due to the huge refractive index of the material. In this work, we demonstrate for the first time the mechanical scanning probe lithography method for the realization of low-cost room-temperature exciton-polariton systems based on the 2D perovskite (PEA)_2PbI_4 with exciton binding energy exceeding 200 meV. Precisely controlling the lithography parameters, we broadly adjust the exciton-polariton dispersion and radiative losses of polaritonic modes in the range of 0.1 to 0.2 of total optical losses. Our findings represent a versatile approach to the fabrication of planar high-quality perovskite-based photonic cavities supporting the strong light-matter coupling regime for the development of on-chip all-optical active and nonlinear polaritonic devices.

We study an autonomous model of a Maxwell demon that works by rectifying thermal fluctuations of chemical reactions. It constitutes the chemical analog of a recently studied electronic demon. We characterize its scaling behavior in the macroscopic limit, its performances, and the impact of potential internal delays. We obtain analytical expressions for all quantities of interest, namely, the generated reverse chemical current, the output power, the transduction efficiency, and the correlations between the numbers of molecules. Due to a bound on the nonequilibrium response of its chemical reaction network, we find that, contrary to the electronic case, there is no way for the Maxwell demon to generate a finite output in the macroscopic limit. Finally, we analyze the information thermodynamics of the Maxwell demon from a bipartite perspective. In the limit of a fast demon, the information flow is obtained, its pattern in the state space is discussed, and the behavior of the partial efficiencies related to the measurement and the feedback processes is examined.

Continuous cellular automata are rocketing in popularity, yet developing a theoretical understanding of their behaviour remains a challenge. In the case of Lenia, a few fundamental open problems include determining what exactly constitutes a soliton, what is the overall structure of the parameter space, and where do the solitons occur in it. In this abstract, we present a new method to automatically classify Lenia systems into four qualitatively different dynamical classes. This allows us to detect moving solitons, and to provide an interactive visualization of Lenia's parameter space structure on our website https://lenia-explorer.vercel.app/. The results shed new light on the above-mentioned questions and lead to several observations: the existence of new soliton families for parameters where they were not believed to exist, or the universality of the phase space structure across various kernels.

We theoretically investigate the phase sensitivity with parity detection on an SU(1,1) interferometer with a coherent state combined with a squeezed vacuum state. This interferometer is formed with two parametric amplifiers for beam splitting and recombination instead of beam splitters. We show that the sensitivity of estimation phase approaches Heisenberg limit and give the corresponding optimal condition. Moreover, we derive the quantum Cram\'er-Rao bound of the SU(1,1) interferometer.

A cylindrical TM_{0,1,0} mode microwave cavity resonator was excited using a balanced interferometric configuration that allowed manipulation of the electric field and potential within the resonator by adjusting the phase and amplitude of the interferometer arms driving the resonator. With precise tuning of the phase and amplitude, 25 dB suppression of the electric field at the resonance frequency was achieved while simultaneously resonantly enhancing the time-varying electric-scalar potential. Under these conditions, the system demonstrated electromagnetically induced absorption in the cavity response due to the annulment of the electric field at the resonance frequency. This phenomena can be regarded as a form of extreme dispersion, and led to a sharp increase in the cavity phase versus frequency response by an order of magnitude when compared to the cavity Q-factor. This work presents an experimental setup that will allow the electric-scalar Aharonov-Bohm effect to be tested under conditions involving a time-varying electric-scalar potential, without the presence of an electric field or magnetic vector potential, an experiment that has not yet been realised.

We study lensing of gravitational waves by a black hole in the deep wave optics regime, i.e. when the wavelength is much larger than the black hole Schwarzschild radius. We apply it to triple systems, with a binary of stellar mass objects in the inspiraling phase orbiting around a central massive black hole. We describe the full polarisation structure of the wave and derive predictions for the polarisation modes of the scattered wave measured by the observer. We show that lensing in the wave optics regime is not helicity preserving, as opposed to lensing in the geometric optics regime. The amplitude of the total wave is modulated due to interference between the directly transmitted and lensed components. The relative amplitude of the modulation is fixed by the lensing geometry and can reach unity in the most favourable settings. This indicates that wave optics lensing is potentially detectable by LISA for sufficiently high SNR systems. Our findings show that in the wave optics regime it is necessary to go beyond the usual lensing description where the amplification factor is assumed to be the same for both helicity modes. While motivated by GW190521 and the AGN formation scenario, our results apply more broadly to stellar-mass binaries orbiting a third body described as a Schwarzschild black hole, with a period comparable to the GW observation time.

We formulate diffractive ring focusing of paraxial beams carrying orbital angular momentum (OAM) through a finite circular aperture as a variational optimization problem. For a fixed topological charge, we determine the real-valued radial pupil that maximizes the intensity at a prescribed ring radius and propagation distance under a normalization constraint on the input field. The resulting problem admits an exact analytical solution: the optimal pupil combines the familiar Fresnel phase structure with an OAM-dependent Bessel radial modulation, and the associated eigenvalue yields a rigorous upper bound on the achievable ring intensity. We further analyze the lens-assisted configuration and derive a simple bound that allows direct comparison between diffractive and refractive vortex focusing. The theory also provides a quantitative framework for evaluating the performance of practical mask designs, including binary Fresnel-Bessel zone plates and amplitude-weighted pupils. We have experimentally tested our predictions in the optical domain by implementing the corresponding vortex beam pupils and comparing their propagation and focusing performance with the optimal solution. Our results establish the vortex-beam analogue of optimal amplitude-only focusing and identify the fundamental limits governing diffractive concentration of structured waves

Sagnac interferometers are important tools for precision measurements. Cancellation of common-path noise ensures a high degree of stability against external perturbations, while their sensitivity to rotations provides the basis of laser gyroscopes. Here we highlight another, less explored feature of Sagnac interferometers: the fact that optical elements are traversed in reverse order for clockwise and counterclockwise propagating light components. This provides the opportunity to explore a classical realization of indefinite causal order, where the order of events within a sequence is not fixed. We explore this concept to identify the geometric phase associated with two non-commuting polarization operations with a single measurement. This idea may have applications for the rapid determination of polarization manipulations or optical activity within chiral media, but foremost it provides a geometric illustration of indefinite causal order.

We study the scalar curvature of the Fisher information metric on the microscopic coupling-parameter manifold of lattice spin models at criticality. For a d-dimensional lattice with periodic boundary conditions and n = L^d sites, the Fisher manifold has m = d cdot n dimensions (one per bond), and we find |R(J_c)| sim n^{d_R} with d_R = (dν+ 2η)/(dν+ η), where ν and η are the correlation-length and anomalous-dimension critical exponents. For 2D Ising (ν= 1, η= 1/4), this predicts d_R = 10/9, confirmed by exact transfer-matrix computations (L = 6--9: d_R = 1.1115 pm 0.0002) and multi-seed MCMC through L = 24. For 3D Ising (ν= 0.630, η= 0.0363), the prediction d_R = 1.019 is consistent with MCMC on L^3 tori up to L = 10 (power-law fit: d_R = 1.040). For 2D Potts q = 3 (predicted 33/29 approx 1.138), FFT-MCMC through L = 40 shows d_eff oscillating non-monotonically around sim 1.20, consistent with O(1/(ln L)^2) logarithmic corrections. For q = 4 (predicted 22/19), effective exponents oscillate with strong logarithmic corrections. The Ricci decomposition identity R_3 = -R_1/2, R_4 = -R_2/2 holds to 5--6 digits for all models. This exponent is distinct from Ruppeiner thermodynamic curvature and reflects the collective geometry of the growing Fisher manifold. We provide falsification criteria and predictions for additional universality classes.

We introduce a platform to achieve ultra-strong coupling (USC) between light and matter using widely available materials. USC is a light-matter interaction regime characterized by coupling strengths exceeding 10% of the ground state energy. It gives rise to novel physical phenomena, such as efficient single-photon coupling and quantum gates, with applications in quantum sensing, nonlinear optics, and low-threshold lasing. Although early demonstrations in plasmonic systems have been realized, achieving USC in dielectric platforms, which offer lower losses and high Q-factors, remains challenging due to typically low mode overlap between the photonic field and the material resonance. Here we leverage dielectric dual gradient metasurfaces supporting quasi-bound states in the continuum to spatially encode both the spectral and coupling parameter space and demonstrate USC to an epsilon-near-zero (ENZ) mode in an ultra-thin SiO2 layer. The strong out-of-plane electric fields in our tapered bar structure overlap exceptionally well with those of the ENZ mode, resulting in a normalized coupling strength of 0.101 and a mode splitting equivalent to 20% of the ENZ mode energy; a four- to five-fold increase compared to previous approaches. The strong field confinement of our approach opens new possibilities for compact and scalable polaritonic devices, such as tunable frequency converters and low-energy optical modulators.

Orbital angular momentum (OAM) multiplexing provides an infinite-dimensional discrete Hilbert space ideally suited for high-capacity free-space quantum key distribution (QKD). Nevertheless, pure scalar spatial modes carrying topological charge (|ell| ge 1) undergo severe decoherence when transmitted through terrestrial atmospheric turbulence. Turbulent refractive-index eddies split high-order vortex singularities, induce catastrophic intermodal crosstalk across adjacent topological channels, and rapidly drive the quantum bit error rate (QBER) well above the unconditional 11% security threshold associated with individual cloning attacks. Here, we demonstrate that hybrid polarization-OAM entangled states, known as vector vortex beams (VVBs), provide intrinsic, hardware-free immunity against turbulent perturbations. Because the optical anisotropy of terrestrial air is exceedingly small (Δn < 10^{-9}), refractive-index fluctuations couple symmetrically to orthogonal circular polarization modes as an identical common-mode scalar phase screen that cancels in the relative polarization-phase degree of freedom. By numerically propagating modal fields through modified power-spectral phase screens over turbulence strengths ranging from D/r_0 = 0 to 3.0, we show that the VVB encoding protocol suppresses the asymptotic QBER from 42.0% to 4.8%, yielding an error-suppression factor of approximately 11.6 without requiring active adaptive optics or deformable mirrors.

Numerical relativity (NR) simulations provide the most faithful representation of the gravitational waves (GWs) emitted by binary black hole (BBH) systems during merger. In the context of GW astronomy, tasks such as parameter estimation can require vast numbers of waveform evaluations per second across the entire parameter space. Since performing full NR simulations for each evaluation is not computationally feasible, interpolating methods for existing NR waveforms, known as surrogate models, have been developed with marked success. In this paper, we build on our previous work to introduce methods to train a fast surrogate model based on neural networks in order to generate BBH merger waveforms, including the fundamental (2,2) mode, as well as the (3,3), (2,1), (4,4), (3,2), (4,3) and (5,5) higher-order modes. Applying a pretraining step on approximant data before fine-tuning on NR data allows us to smooth out the parameter space, and making use of the parallelization ability of GPUs to project the NR waveforms in the inclination-phase (ι, ϕ) sphere during training allows the fitting of all the explored modes simultaneously. The developed surrogate model, DANSur\_HM, achieves average mismatches of the order of 10^{-4}, with the worst mismatch at 2.5times10^{-3}, and achieves throughput above 6times10^5 waveforms/second on an NVIDIA V100 GPU. Parameter estimation tests confirm the usefulness of the inclusion of higher modes.

We discuss the numerical solution of initial value problems for varepsilon^2,varphi''+a(x),varphi=0 in the highly oscillatory regime, i.e., with a(x)>0 and 0<varepsilonll 1. We analyze and implement an approximate solution based on the well-known WKB-ansatz. The resulting approximation error is of magnitude O(varepsilon^{N}) where N refers to the truncation order of the underlying asymptotic series. When the optimal truncation order N_{opt} is chosen, the error behaves like O(varepsilon^{-2}exp(-cvarepsilon^{-1})) with some c>0.

While the popularity of physics-informed neural networks (PINNs) is steadily rising, to this date PINNs have not been successful in simulating dynamical systems whose solution exhibits multi-scale, chaotic or turbulent behavior. In this work we attribute this shortcoming to the inability of existing PINNs formulations to respect the spatio-temporal causal structure that is inherent to the evolution of physical systems. We argue that this is a fundamental limitation and a key source of error that can ultimately steer PINN models to converge towards erroneous solutions. We address this pathology by proposing a simple re-formulation of PINNs loss functions that can explicitly account for physical causality during model training. We demonstrate that this simple modification alone is enough to introduce significant accuracy improvements, as well as a practical quantitative mechanism for assessing the convergence of a PINNs model. We provide state-of-the-art numerical results across a series of benchmarks for which existing PINNs formulations fail, including the chaotic Lorenz system, the Kuramoto-Sivashinsky equation in the chaotic regime, and the Navier-Stokes equations in the turbulent regime. To the best of our knowledge, this is the first time that PINNs have been successful in simulating such systems, introducing new opportunities for their applicability to problems of industrial complexity.

Schrödinger operators with nonlocal δ-interaction are studied with the use of the Lax-Phillips scattering theory methods. The condition of applicability of the Lax-Phillips approach in terms of non-cyclic functions is established. Two formulas for the S-matrix are obtained. The first one deals with the Krein-Naimark resolvent formula and the Weyl-Titchmarsh function, whereas the second one is based on modified reflection and transmission coefficients. The S-matrix S(z) is analytical in the lower half-plane C_- when the Schrödinger operator with nonlocal δ-interaction is positive self-adjoint. Otherwise, S(z) is a meromorphic matrix-valued function in C_- and its properties are closely related to the properties of the corresponding Schrödinger operator. Examples of S-matrices are given.

A set of infinitesimal {rm Virasoro_{,L}}rm Virasoro_{,R} diffeomorphisms are presented which act non-trivially on the horizon of a generic Kerr black hole with spin J. The covariant phase space formalism provides a formula for the Virasoro charges as surface integrals on the horizon. Integrability and associativity of the charge algebra are shown to require the inclusion of `Wald-Zoupas' counterterms. A counterterm satisfying the known consistency requirement is constructed and yields central charges c_L=c_R=12J. Assuming the existence of a quantum Hilbert space on which these charges generate the symmetries, as well as the applicability of the Cardy formula, the central charges reproduce the macroscopic area-entropy law for generic Kerr black holes.

We introduce physics informed neural networks -- neural networks that are trained to solve supervised learning tasks while respecting any given law of physics described by general nonlinear partial differential equations. In this two part treatise, we present our developments in the context of solving two main classes of problems: data-driven solution and data-driven discovery of partial differential equations. Depending on the nature and arrangement of the available data, we devise two distinct classes of algorithms, namely continuous time and discrete time models. The resulting neural networks form a new class of data-efficient universal function approximators that naturally encode any underlying physical laws as prior information. In this first part, we demonstrate how these networks can be used to infer solutions to partial differential equations, and obtain physics-informed surrogate models that are fully differentiable with respect to all input coordinates and free parameters.

All known up to now models of chemical oscillations are based exclusively on kinetic considerations. The chemical gross-process equation is split usually by elementary steps, each step is supplied by an arrow and a differential equation, joint solution to such a construction under certain, often ad hoc chosen conditions and with ad hoc numerical coefficients leads to chemical oscillations. Kinetic perception of chemical oscillations reigns without exclusions. However, as it was recently shown by the author for the laser and for the electrochemical systems, chemical oscillations follow also from solutions to the basic expressions of discrete thermodynamics of chemical equilibria. Graphically those solutions are various fork bifurcation diagrams, and, in certain types of chemical systems, oscillations are well pronounced in the bistable bifurcation areas. In this work we describe a general thermodynamic approach to chemical oscillations as opposite to kinetic models, and depict some of their new features like spontaneity and fractality. The paper doubts exclusivity of the kinetic approach to chemical oscillations, and its aim is to discuss and exemplify thermodynamically predicted chemical oscillations in closed chemical systems.

We study the bi-parameter local linearization of the one-dimensional nonlinear stochastic wave equation driven by a Gaussian noise, which is white in time and has a spatially homogeneous covariance structure of Riesz-kernel type. We establish that the second-order increments of the solution can be approximated by those of the corresponding linearized wave equation, modulated by the diffusion coefficient. These findings extend the previous results of Huang et al. HOO2024, which addressed the case of space-time white noise. As applications, we analyze the quadratic variation of the solution and construct a consistent estimator for the diffusion parameter.

The dynamical realisation of the equation of state p +rho =0 is studied. A non-pathological dynamics for the perturbations of such a system mimicking a dynamical cosmological constant (DCC) requires to go beyond the perfect fluid paradigm. It is shown that an anisotropic stress must be always present. The Hamiltonian of the system in isolation resembles the one of a Pais-Uhlenbeck oscillator and linear stability requires that it cannot be positive definite. The dynamics of linear cosmological perturbations in a DCC dominated Universe is studied in detail showing that when DCC is minimally coupled to gravity no dramatic instability is present. In contrast to what happens in a cosmological constant dominated Universe, the non-relativistic matter contrast is no longer constant and exhibits an oscillator behaviour at small scales while it grows weakly at large scales. In the gravitational waves sector, at small scales, the amplitude is still suppressed as the inverse power of the scale factor while it grows logarithmically at large scales. Also the vector modes propagate, though no growing mode is found.

In this paper, we investigate the behavior of gradient descent algorithms in physics-informed machine learning methods like PINNs, which minimize residuals connected to partial differential equations (PDEs). Our key result is that the difficulty in training these models is closely related to the conditioning of a specific differential operator. This operator, in turn, is associated to the Hermitian square of the differential operator of the underlying PDE. If this operator is ill-conditioned, it results in slow or infeasible training. Therefore, preconditioning this operator is crucial. We employ both rigorous mathematical analysis and empirical evaluations to investigate various strategies, explaining how they better condition this critical operator, and consequently improve training.

Unmanned vehicle navigation concerns estimating attitude, position, and linear velocity of the vehicle the six degrees of freedom (6 DoF). It has been known that the true navigation dynamics are highly nonlinear modeled on the Lie Group of SE_{2}(3). In this paper, a nonlinear filter for inertial navigation is proposed. The filter ensures systematic convergence of the error components starting from almost any initial condition. Also, the errors converge asymptotically to the origin. Experimental results validates the robustness of the proposed filter.

We introduce a data-driven diagnostic that combines the singular value decomposition (SVD) with an information-theoretic entropy to quantify the phase-space complexity of perturbed distribution functions in gyrokinetic turbulence. Applying this framework to nonlinear flux-tube simulations that solve the time evolution of the ion distribution function represented by Fourier modes with the wavenumber for real space, we define the von Neumann entropy (vNE) to analyze the velocity-space structure. A global survey in the wavenumber space reveals a wavenumber-dependent variation of the vNE in velocity-space structure: the vNE remains low at low wavenumber but increases across k_perpρ_{ti}sim 1. Hermite/Laguerre decompositions revealed that the finite Larmor radius (FLR) phase mixing in the perpendicular (magnetic-moment) direction is active. Simultaneously, the systematic increase in vNE for k_perpρ_{ti} correlates with the broadening of the Hermite spectrum, suggesting enhanced parallel phase mixing (Landau resonance) as the primary mechanism for the observed wave number dependence. These results demonstrate that the SVD-based vNE provides a compact measure of kinetic complexity without assuming a predefined basis and enables a global mapping of its wavenumber dependence of phase-mixing processes in gyrokinetic turbulence.

Artificial transmission lines built with lumped-element inductors and capacitors form the backbone of broadband, nearly quantum-limited traveling-wave parametric amplifiers (TWPAs). However, systematic design methods for TWPAs, and more generally artificial transmission lines, are lacking. Here, I develop a general synthesis framework for lossless artificial transmission lines by borrowing from periodic structure theory and passive network synthesis. These complementary approaches divide the design space: periodic loading synthesis employs spatial modulation of frequency-independent components, while filter synthesis employs frequency-dependent responses in spatially-uniform components. When tailoring transmission lines for parametric processes, nonlinear elements are added, typically nonlinear inductances in superconducting circuits, while ensuring energy and momentum conservation between interacting tones. Applying this framework, I design a kinetic inductance TWPA with a novel phase-matching architecture, and a backward-pumped Josephson TWPA exploiting an ambidextrous i.e., right-left-handed transmission line.

Achieving robust high-dimensional solitons both in optics and Bose-Einstein condensates remains a great challenge, due to unpredictable high-order perturbations. Here we propose and demonstrate a novel topological spatiotemporal mode-locked fiber laser empowered by mode-division multiplexing, for precisely controlling of the spatiotemporal solitons. By introducing time delays between the individual transverse mode paths, a topological spatiotemporal lattice is formed in the multimode cavity, which in turn excites periodic spatiotemporal solitons. These solitons are stable against the perturbations, attributed to periodic potentials induced by the nonreciprocal dissipative coupling interactions. Moreover, under the thermodynamic limit, the solitons condense into nested-type spatiotemporal solitons, a phenomenon analogous to the Bose-Einstein condensate of matter waves. Our results indicate that topological spatiotemporal mode-locked lasers not only constitute a controllable source of robust spatiotemporal light bullets, but also provide a valuable platform for exploring nonlinear high-dimensional soliton dynamics and non-Hermitian topological physics.

We present the new public version of the KETJU supermassive black hole (SMBH) dynamics module, as implemented into GADGET-4. KETJU adds a small region around each SMBH where the dynamics of the SMBHs and stellar particles are integrated using an algorithmically regularised integrator instead of the leapfrog integrator with gravitational softening used by GADGET-4. This enables modelling SMBHs as point particles even during close interactions with stellar particles or other SMBHs, effectively removing the spatial resolution limitation caused by gravitational softening. KETJU also includes post-Newtonian corrections, which allows following the dynamics of SMBH binaries to sub-parsec scales and down to tens of Schwarzschild radii. Systems with multiple SMBHs are also supported, with the code also including the leading non-linear cross terms that appear in the post-Newtonian equations for such systems. We present tests of the code showing that it correctly captures, at sufficient mass resolution, the sinking driven by dynamical friction and binary hardening driven by stellar scattering. We also present an example application demonstrating how the code can be applied to study the dynamics of SMBHs in mergers of multiple galaxies and the effect they have on the properties of the surrounding galaxy. We expect that the presented KETJU SMBH dynamics module can also be straightforwardly incorporated into other codes similar to GADGET-4, which would allow coupling small-scale SMBH dynamics to the rich variety of galactic physics models that exist in the literature.

This paper describes a method for learning low-dimensional approximations of nonlinear dynamical systems, based on neural-network approximations of the underlying Koopman operator. Extended Dynamic Mode Decomposition (EDMD) provides a useful data-driven approximation of the Koopman operator for analyzing dynamical systems. This paper addresses a fundamental problem associated with EDMD: a trade-off between representational capacity of the dictionary and over-fitting due to insufficient data. A new neural network architecture combining an autoencoder with linear recurrent dynamics in the encoded state is used to learn a low-dimensional and highly informative Koopman-invariant subspace of observables. A method is also presented for balanced model reduction of over-specified EDMD systems in feature space. Nonlinear reconstruction using partially linear multi-kernel regression aims to improve reconstruction accuracy from the low-dimensional state when the data has complex but intrinsically low-dimensional structure. The techniques demonstrate the ability to identify Koopman eigenfunctions of the unforced Duffing equation, create accurate low-dimensional models of an unstable cylinder wake flow, and make short-time predictions of the chaotic Kuramoto-Sivashinsky equation.

We present the analytic evaluation of the gravitational energy and of the angular momentum flux with tidal effects for inspiraling compact binaries, at next-to-next-to-leading post-Newtoian (2PN) order, within the effective field theory diagrammatic approach. We first compute the stress-energy tensor for a binary system, that requires the evaluation of two-point Feynman integrals, up to two loops. Then, we extract the multipole moments of the system, which we present for generic orbits in center-of-mass coordinates, and which are needed for the evaluation of the total gravitational energy and the angular momentum flux, for generic orbits. Finally, we provide the expression of gauge invariant quantities such as the fluxes, and the mode amplitudes and phase of the emitted gravitational wave, for circular orbits. Our findings are useful to update earlier theoretical studies as well as related phenomenological analyses, and waveform models

The phase evolution of gravitational waves encodes critical information about the orbital dynamics of binary systems. In this work, we test the robustness of parameterized tests against unmodeled deviations from general relativity. We demonstrate that these parameterized tests are flexible and sensitive in detecting generic deviations in the waveform using the Cutler-Vallisneri bias formalism. This universality arises from examining the inherent geometry of the waveform signal and understanding how biases manifest. We show how Bayes factors are governed by the intrinsic geometry of the waveform signal manifold when parameterized tests are used to approximate generic violations of GR. We use the singular value decomposition to propose templates that are orthogonal to parameterized tests, identifying degeneracies and enhancing the detection of potential deviations. More broadly, the geometric framework developed here clarifies -- at a fundamental level -- how subtle waveform effects (including orbital eccentricity, spin precession, waveform systematics, and instrumental glitches) can mimic one another in data, and when they are intrinsically distinguishable.

We present a survey of the many and various elements of the modern higher-dimensional theory of quasiconformal mappings and their wide and varied application. It is unified (and limited) by the theme of the author's interests. Thus we will discuss the basic theory as it developed in the 1960s in the early work of F.W. Gehring and Yu G. Reshetnyak and subsequently explore the connections with geometric function theory, nonlinear partial differential equations, differential and geometric topology and dynamics as they ensued over the following decades. We give few proofs as we try to outline the major results of the area and current research themes. We do not strive to present these results in maximal generality, as to achieve this considerable technical knowledge would be necessary of the reader. We have tried to give a feel of where the area is, what are the central ideas and problems and where are the major current interactions with researchers in other areas. We have also added a bit of history here and there. We have not been able to cover the many recent advances generalising the theory to mappings of finite distortion and to degenerate elliptic Beltrami systems which connects the theory closely with the calculus of variations and nonlinear elasticity, nonlinear Hodge theory and related areas, although the reader may see shadows of this aspect in parts.

In the present paper we study the singularity structure of the exterior field of neutron stars with the aid of the four-parameter exact solution of the Einstein-Maxwell equations. The complete analysis of this problem in the generic case becomes possible due to the implementation of the novel analytical approach to the resolution of the singularity condition, and it shows the absence of the ring singularities off the symmetry axis in the positive mass case, as well as the possibility of the removal of the ring singularity by a strong magnetic field in the negative mass case. The solution takes an extraordinarily simple form in the equatorial plane, very similar to that of the Kerr solution, which makes it most suitable for astrophysical applications as the simplest model of a rotating magnetized deformed mass. It also provides a nontrivial example confirming a recent claim that the varphi component of the electromagnetic four-potential has features inconsistent with the intrinsic properties of the electrovac metric, while the magnetic field is represented correctly by the t component of the dual electromagnetic four-potential.

In this manuscript we set up the direct and inverse scattering problems for step-like traveling-wave solutions of the nonlinear Schrödinger equation. Specifically, we consider initial data u(x,0) satisfying u(x,0)to u_0^ell(x) as xto-infty and u(x,0)to u_0^r(x) as xto+infty, where u_0^ell(x) and u_0^r(x) are elliptic traveling waves. Under suitable assumptions on the initial data we formulate the direct scattering problem and establish analytic properties of the scattering data. We then formulate the inverse problem as a Riemann--Hilbert problem and prove its solvability. Finally, we observe that this Riemann--Hilbert formulation is a special case of the one arising for full soliton-gas initial data.

We review the unconventional photon blockade mechanism. This quantum effect remarkably enables a strongly sub-Poissonian light statistics, even from a system characterized by a weak single photon nonlinearity. We revisit the past results, which can be interpreted in terms of quantum interferences or optimal squeezing, and show how recent developments on input-output field mixing can overcome the limitations of the original schemes towards passive and integrable single photon sources. We finally present some valuable alternative schemes for which the unconventional blockade can be directly adapted.

Initial value problems -- a system of ordinary differential equations and corresponding initial conditions -- can be used to describe many physical phenomena including those arise in classical mechanics. We have developed a novel approach to solve physics-based initial value problems using unsupervised machine learning. We propose a deep learning framework that models the dynamics of a variety of mechanical systems through neural networks. Our framework is flexible, allowing us to solve non-linear, coupled, and chaotic dynamical systems. We demonstrate the effectiveness of our approach on systems including a free particle, a particle in a gravitational field, a classical pendulum, and the H\'enon--Heiles system (a pair of coupled harmonic oscillators with a non-linear perturbation, used in celestial mechanics). Our results show that deep neural networks can successfully approximate solutions to these problems, producing trajectories which conserve physical properties such as energy and those with stationary action. We note that probabilistic activation functions, as defined in this paper, are required to learn any solutions of initial value problems in their strictest sense, and we introduce coupled neural networks to learn solutions of coupled systems.

Large nonlinear recurrent neural networks with random couplings generate high-dimensional, potentially chaotic activity whose structure is of interest in neuroscience and other fields. A fundamental object encoding the collective structure of this activity is the N times N covariance matrix. Prior analytical work on the covariance matrix has been limited to low-dimensional summary statistics. Recent work proposed an ansatz in which, at large N, the covariance matrix for a typical quenched realization takes the same form as that of a linear network with the same couplings, driven by independent noise, with DMFT order parameters setting the transfer function and the noise spectrum. Here, we derive this ansatz using the two-site cavity method, providing two derivations with complementary perspectives. The first decomposes each unit's activity into a linear response to its local field and a nonlinear residual, and shows that cross-covariances between residuals at distinct sites are strongly suppressed, so the residuals act as independent noise driving a linear network. The second derives a self-consistent matrix equation for the covariance matrix. A naive Gaussian closure for the joint statistics of local fields at distinct sites misses cross terms that, in a linear network, would be generated by an external drive. The cavity method recovers these terms from non-Gaussian contributions, revealing an emergent external drive. Higher-order cross-site moments follow a Wick-like decomposition into products of pairwise covariances at leading order, reducing them to the linear-equivalent form. We verify the predictions in simulations. These results extend linear equivalence from feedforward high-dimensional nonlinear systems, where the activations are independent of the weights, to recurrent networks, where the activations are correlated with the couplings that generate them.

Outer-learning algorithms use infinitesimal sensitivities to propose finite changes to initialization or training parameters. For hard-ReLU training, the derivative of the finite program and the derivative of its flow limit do not by themselves specify the response at a chosen radius. We characterize the intervening regime in which the perturbation radius is proportional to the GD step. Integer event rounding then survives at leading order: smooth Euler bias shifts each discrete phase, and upstream rounding moves downstream branch boundaries. We derive the crossing indices and a uniform endpoint expansion for finitely many separated transverse events in piecewise-C^2 dynamics, away from recursive phase boundaries. In contractive affine regions, an explicit remainder and complete branch verification certify finite candidate comparisons. Scalar phase frequencies and a coupled feedback ablation test the mechanism; frozen nonlinear-network experiments show radius-dependent prediction accuracy, including incomplete branch matches and failed-word tails. Together with local AD and uniform flow consistency, the result identifies sufficient response regimes: differentiating training is a choice of perturbation resolution as well as a choice of derivative.

This work investigates the number of limit cycles bifurcating from the periodic orbits of a linear center when it is perturbed by piecewise holomorphic systems with three zones separated by two external circles. We analyze how different geometric configurations of these zones influence the number of limit cycles. Moreover, we show the existence of at least sixteen limit cycles in fourth-degree piecewise polynomial holomorphic systems under certain configurations.

Using the supersymmetric method of random matrix theory within the Heidelberg approach framework we provide statistical description of stationary intensity sampled in locations inside an open wave-chaotic cavity, assuming that the time-reversal invariance inside the cavity is fully broken. In particular, we show that when incoming waves are fed via a finite number M of open channels the probability density {cal P}(I) for the single-point intensity I decays as a power law for large intensities: {cal P}(I)sim I^{-(M+2)}, provided there is no internal losses. This behaviour is in marked difference with the Rayleigh law {cal P}(I)sim exp(-I/I) which turns out to be valid only in the limit Mto infty. We also find the joint probability density of intensities I_1, ldots, I_L in L>1 observation points, and then extract the corresponding statistics for the maximal intensity in the observation pattern. For Lto infty the resulting limiting extreme value statistics (EVS) turns out to be different from the classical EVS distributions.

We investigate gravitational-wave echoes in a horizonless compact object model, a non-perturbative solution of the semi-classical Einstein equation that reproduces the entropy-area law from the bulk structure. By employing a model of anisotropic fluids in classical general relativity (GR), we show that odd-parity gravitational waves are not reflected at the object's surface but are trapped inside due to the exponentially strong redshift, and that the echo-delay time extremely exceeds the age of the Universe. Consequently, the echo signals are effectively unobservable, which is consistent with current null results from echo searches. We finally discuss how this quantum black hole and the conventional classical black hole could be distinguished observationally.

We consider a Schr\"odinger-Poisson system involving a general nonlinearity at critical growth and we prove the existence of positive solutions. The Ambrosetti-Rabinowitz condition is not required. We also study the asymptotics of solutions with respect to a parameter.

The Rayleigh-Plateau instability predicts that infinitesimal perturbations of a liquid jet grow only for kR < 1, with kR = 1 marking the classical stability boundary. Here, we show that femtosecond-laser-induced cavitation generates a localized, impulsive recoil perturbation on a flowing liquid jet, enabling a two-dimensional map of jet breakup across the (kR, epsilon/R) plane. The perturbation's spacing (wavelength) and strength (amplitude) are set independently by the laser repetition rate and pulse energy, respectively. At low amplitudes, tuning the repetition rate recovers the classical Rayleigh-Plateau dispersion relation and its kR = 1 cutoff, while increasing the wavelength enables controlled generation of monodisperse droplet trains, bidisperse droplet populations, and ultimately isolated single droplets. Along the amplitude axis, low pulse energies produce a seed that amplifies only the imposed wavenumber, whereas above a critical energy Ec, the seed broadens to excite many wavenumbers simultaneously. At still higher amplitudes, we demonstrate deterministic breakup for kR > 1, extending to kR = 1.9, with laser-synchronized droplet production rates up to 0.2 MHz. These results establish localized femtosecond-laser-induced cavitation as a route to controlled Rayleigh-Plateau breakup both within and beyond the classical linear-stability boundary.

In the framework of Scalar-Tensor-Vector Gravity (STVG), this paper investigates the quasinormal modes and time-domain evolution of Reissner-Nordström Modified Gravity (MOG) black holes under massless scalar, electromagnetic, and gravitational perturbations. Quasinormal frequencies are calculated by extending the 3rd- to 6th-order WKB method and combining it with Padé approximation to the 13th order, while complete time-domain waveforms are obtained using a finite-difference method based on light-cone coordinates. The results indicate that increasing the MOG parameter α raises the effective mass of the black holes, leading to a decrease in the damping rate |ω_I| and a slower ringdown decay. An increase in charge Q produces a similar effect, with the damping approaching zero in the near-extremal limit. Regarding the ringdown decay times for the three types of perturbations, the gravitational field has the longest duration, the electromagnetic field is intermediate, and the scalar field is the shortest. The oscillations and decay observed in the time-domain waveforms are qualitatively consistent with the frequency-domain results, and the power-law exponent governing the late-time tail aligns with that of asymptotically flat spacetimes. This study provides a systematic theoretical reference for testing modified gravity theories using black hole spectroscopy.

We present a web-based software tool, the Virtual Quantum Optics Laboratory (VQOL), that may be used for designing and executing realistic simulations of quantum optics experiments. A graphical user interface allows one to rapidly build and configure a variety of different optical experiments, while the runtime environment provides unique capabilities for visualization and analysis. All standard linear optical components are available as well as sources of thermal, coherent, and entangled Gaussian states. A unique aspect of VQOL is the introduction of non-Gaussian measurements using detectors modeled as deterministic devices that "click" when the amplitude of the light falls above a given threshold. We describe the underlying theoretical models and provide several illustrative examples. We find that VQOL provides a a faithful representation of many experimental quantum optics phenomena and may serve as both a useful instructional tool for students as well as a valuable research tool for practitioners.

In this paper, we first study the consequence of spacetime translations and Lorentz transformations on Celestial CFT OPEs. Working with the light transforms of the operators belonging to the modified Mellin basis, we found that the leading order singularity in the OPE of such operators could be fixed purely using Poincaré symmetries owing to the non-trivial action of the translations on these operators. The OPE coefficient is then fixed using the soft limit of the correlation functions. We check that this singular structure obtained from symmetries is consistent with the OPE limit of three-point functions. This approach could potentially be useful for studying Celestial CFT without adverting to bulk physics. As another goal, we explore the significance of light transformation in Carrollian CFTs. In the special cases we considered, we show that light transformation equips us with a map between two branches of Carroll CFT in d=3 dimension at the level of correlation functions in the near coincident limit.

An electro-optic modulator offers the function of modulating the propagation of light in a material with electric field and enables seamless connection between electronics-based computing and photonics-based communication. The search for materials with large electro-optic coefficients and low optical loss is critical to increase the efficiency and minimize the size of electro-optic devices. We present a semi-empirical method to compute the electro-optic coefficients of ferroelectric materials by combining first-principles density-functional theory calculations with Landau-Devonshire phenomenological modeling. We apply the method to study the electro-optic constants, also called Pockels coefficients, of three paradigmatic ferroelectric oxides: BaTiO3, LiNbO3, and LiTaO3. We present their temperature-, frequency- and strain-dependent electro-optic tensors calculated using our method. The predicted electro-optic constants agree with the experimental results, where available, and provide benchmarks for experimental verification.

Even for known nonlinear dynamical systems, feedback controller synthesis is a difficult problem that often requires leveraging the particular structure of the dynamics to induce a stable closed-loop system. For general nonlinear models, including those fit to data, there may not be enough known structure to reliably synthesize a stabilizing feedback controller. In this paper, we discuss a state-dependent nonlinear tracking controller formulation based on a state-dependent Riccati equation for general nonlinear control-affine systems. This formulation depends on a nonlinear factorization of the system of vector fields defining the control-affine dynamics, which always exists under mild smoothness assumptions. We propose a method for learning this factorization from a finite set of data. On a variety of simulated nonlinear dynamical systems, we empirically demonstrate the efficacy of learned versions of this controller in stable trajectory tracking. Alongside our learning method, we evaluate recent ideas in jointly learning a controller and stabilizability certificate for known dynamical systems; we show experimentally that such methods can be frail in comparison.

In this study, we propose a multi branched network approach to predict the dynamics of a physics attractor characterized by intricate and chaotic behavior. We introduce a unique neural network architecture comprised of Radial Basis Function (RBF) layers combined with an attention mechanism designed to effectively capture nonlinear inter-dependencies inherent in the attractor's temporal evolution. Our results demonstrate successful prediction of the attractor's trajectory across 100 predictions made using a real-world dataset of 36,700 time-series observations encompassing approximately 28 minutes of activity. To further illustrate the performance of our proposed technique, we provide comprehensive visualizations depicting the attractor's original and predicted behaviors alongside quantitative measures comparing observed versus estimated outcomes. Overall, this work showcases the potential of advanced machine learning algorithms in elucidating hidden structures in complex physical systems while offering practical applications in various domains requiring accurate short-term forecasting capabilities.

We consider Proca field perturbations in a five-dimensional Schwarzschild-anti-de Sitter (Schwarzschild-AdS_{5}) black hole geometry. Using the vector spherical harmonic (VSH) method, we show that the Proca field decomposes into scalar-type and vector-type components according to their tensorial behavior on the three-sphere. Two degrees of freedom of the field are described by scalar-type components, which are coupled due to the mass term, while the remaining two degrees of freedom are described by a vector-type component, which decouples completely. Motivated by the Frolov-Krtouš-Kubizňák-Santos (FKKS) ansatz in the limit of zero spin, we use a field transformation to decouple the scalar-type components at the expense of introducing a complex separation parameter β. This parameter can be determined analytically, and its values correspond to two distinct polarizations of the scalar-type sector: "electromagnetic" and "non-electromagnetic", denoted by β_{+} and β_{-}, respectively. In the scalar-type sector, the radial differential equation for each polarization is a Fuchsian differential equation with five singularities, whereas in the vector-type sector, the radial equation has four singularities. By means of the isomonodromy method, we reformulate the boundary value problem in terms of the initial conditions of the Painlevé VI τ function and, using a series expansion of the τ function, we compute the scalar-type and vector-type quasinormal modes (QNMs) in the small horizon limit. Our results are in overall very good agreement with those obtained via the numerical integration method. This shows that the isomonodromy method is a reliable method to compute quasinormal modes in the small horizon limit with high accuracy.

High-accuracy microwave sensing is widely demanded in various fields, ranging from cosmology to microwave quantum technology. Quantum receivers based on inorganic solid-state spin systems are promising candidates for such purpose because of the stability and compatibility, but their best sensitivity is currently limited to a few pT/rm{Hz}. Here, by utilising an enhanced readout scheme with the state-of-the-art solid-state maser technology, we develop a robust microwave quantum receiver functioned by organic molecular spins at ambient conditions. Owing to the maser amplification, the sensitivity of the receiver achieves 6.14 pm 0.17 fT/rm{Hz} which exceeds three orders of magnitude than that of the inorganic solid-state quantum receivers. The heterodyne detection without additional local oscillators improves bandwidth of the receiver and allows frequency detection. The scheme can be extended to other solid-state spin systems without complicated control pulses and thus enables practical applications such as electron spin resonance spectroscopy, dark matter searches, and astronomical observations.

We investigate the effects of quantum geometry on the motion of magnon wave packets in one-dimensional quantum spin chains. In contrast to fermionic systems, where transport phenomena driven by the quantum metric have been extensively studied, we show that the dynamics in bosonic magnon systems are strongly affected by the symplectic structure and the pseudo-unitarity of the transformation of the magnon Bogoliubov-de Gennes Hamiltonian. A chiral soliton lattice provides a setting in which the symplectic quantum metric strongly influences the longitudinal magnon dynamics. We derive the semiclassical response of a magnon wave packet in such a system to a weak, slowly varying perturbation and demonstrate that the wave packet velocity acquires a geometric contribution proportional to the momentum derivative of the symplectic quantum metric, which dominates over the conventional group velocity for a nearly flat band. Solving the resulting equations of motion, we obtain a bounded trajectory in real time with a phase-space area determined by the symplectic quantum metric.

In the axion model, electromagnetic waves interacting with axions induce frequency-dependent time delays, determined by the axion mass and decay constant. These small delays are difficult to detect, making traditional methods ineffective. To address this, we computed time delays for various parameters and found a prominent dispersion signal when the wave frequency equals half the axion mass. Based on this, we developed a machine learning-based pipeline, achieving 95\% classification accuracy and demonstrating strong detection capability in low signal-to-noise data. Applying this to PSR J1933-6211, we found no axion-induced delays within current sensitivity limits. While existing constraints are limited by atomic clock resolution in radio telescopes, future advances in optical clocks and broader bandwidths will enable more extensive searches. In particular, combining high-precision optical clocks with next-generation radio telescopes, such as the Qitai Radio Telescope, could improve decay constant constraints by four orders of magnitude for axion masses in the 10^{-6} sim 10^{-4} eV range.

High Power Laser's (HPL) optimal performance is essential for the success of a wide variety of experimental tasks related to light-matter interactions. Traditionally, HPL parameters are optimised in an automated fashion relying on black-box numerical methods. However, these can be demanding in terms of computational resources and usually disregard transient and complex dynamics. Model-free Deep Reinforcement Learning (DRL) offers a promising alternative framework for optimising HPL performance since it allows to tune the control parameters as a function of system states subject to nonlinear temporal dynamics without requiring an explicit dynamics model of those. Furthermore, DRL aims to find an optimal control policy rather than a static parameter configuration, particularly suitable for dynamic processes involving sequential decision-making. This is particularly relevant as laser systems are typically characterised by dynamic rather than static traits. Hence the need for a strategy to choose the control applied based on the current context instead of one single optimal control configuration. This paper investigates the potential of DRL in improving the efficiency and safety of HPL control systems. We apply this technique to optimise the temporal profile of laser pulses in the L1 pump laser hosted at the ELI Beamlines facility. We show how to adapt DRL to the setting of spectral phase control by solely tuning dispersion coefficients of the spectral phase and reaching pulses similar to transform limited with full-width at half-maximum (FWHM) of ca1.6 ps.