Under study in this paper is a nonlinear Schrödinger equation with local and nonlocal nonlinearities, which originates from the parity-symmetric reduction of the Manakov system and has applications in some physical systems with the parity symmetry constraint between two fields/components. Via the Riemann-Hilbert method, the theory of inverse scattering transform with the presence of double poles is extended for this equation under nonzero boundary conditions (NZBCs). Also, the double-pole soliton solutions with NZBCs are derived in the reflectionless case. It is shown that the quasi-periodic beating solitons can be obtained when the double pole lies off the circle $\Gamma$ centered at the origin with radius $\sqrt{2}{q}_{0}$ (where q₀ is the modulus of NZBCs) on the spectrum plane. Moreover, using the improved asymptotic analysis method, the asymptotic solitons are found to be located in some logarithmic curves of the xt plane.

In this study, we propose that many different thermodynamic modeling approaches, including the general equation for the non-equilibrium reversible-irreversible coupling (GENERIC), Onsager's variational principle, the energetic variational approach, and classical irreversible thermodynamics, can all be cast into the gradient-conservative structure (GCS). GCS enjoys many nice mathematical properties, has close connection with the large deviations principle and gradient flows in Wasserstein space, and fulfills laws of thermodynamics. Our results demonstrate that the GCS may serve as a unified theoretical framework to model various non-equilibrium thermodynamic processes.

We establish a quantum dynamics framework for curved submanifolds embedded in higher-dimensional spaces. Through rigorous dimensional reduction, we derive the first complete Schrödinger and Klein-Gordon equations incorporating non-perturbative geometric interactions-resolving ambiguities in constrained quantization. Crucially, extrinsic curvature of the ambient manifold governs emergent low-dimensional quantum phenomena. Remarkably, this mechanism generates scalar field masses matching Kaluza-Klein spectra while eliminating periodic compactification Requirements. We hypothesize that geometric induction can produce Higgs-mechanism-type potentials. Under this working hypothesis, particle masses arise solely from submanifold embedding geometry and matter-field couplings are encoded in curvature invariants. If this hypothesis holds, it would enable experimental access to higher-dimensional physics at all energy scales through geometric induction. We also discuss the Higgs vacuum near small-mass black holes.

In this work, we propose a new deep learning approach based on physics-informed neural networks (PINNs), termed parallel parity-time-symmetric PINNs (PPTS-PINNs), to address the inverse problem of determining the PT-symmetric potential function in the nonlinear Schrödinger equation (NLSE). By incorporating PT-symmetry constraints and a gradient enhancement strategy, the method effectively improves both the accuracy and stability of solving inverse problems, while preserving the consistency of the physical structure. We conduct systematic numerical experiments on two representative NLSEs under both noise-free and noisy conditions (with noise levels of 1% and 5%) to evaluate the reconstruction performance of the model given fixed observational data. The results demonstrate that PPTS-PINNs can robustly reconstruct the complex-valued potential function across different noise levels, achieving an overall error on the order of 10^-3. Notably, under high-noise conditions, the combination of PT-symmetry constraints and the gradient enhancement strategy significantly enhances the model's robustness by mitigating error propagation. Overall, the proposed method exhibits strong adaptability and generalization capabilities in PT-symmetric modeling and noise-resilient learning, offering a novel perspective for solving more complex physical inverse problems.

In this article, the large-time asymptotic wave dynamics of rogue curves are analytically investigated and numerically confirmed in the Davey-Stewartson (DS) I equation. We show that, when time in bilinear expressions of the rogue curves is large, a certain number of localized lump-shaped waves would arise on the uniform background, exhibiting various wave patterns. We further show that, as time increases, the individual lump-shaped wave asymptotically evolves into a line soliton on the constant background that persist at large time. By performing large-time asymptotic analysis, we reveal that such wave patterns as well as the numbers of lump-shaped waves can be analytically determined by the structure of nonzero roots of the Wronskian-Hermite polynomials. Our asymptotic predictions are compared to true solutions quantitatively and excellent agreement is obtained.

We investigate the dynamics of a two-level quantum system driven by a laser pulse characterized by Lorentzian frequency and sub-Lorentzian amplitude modulations. Complete analytical solutions, expressed via confluent Heun functions, are derived. Our analysis reveals that explicit exact analytical solutions exist under infinite sets of specific parameter conditions. The effects of modulation parameters and initial conditions on the final transition probabilities are examined analytically and numerically. Furthermore, the method is demonstrated to be directly applicable to two closely related models with Lorentzian pulses.

Both axion and dark photon dark matter are among the most promising candidates of dark matter. What we know with some confidence is that they exhibit a small velocity distribution δv $\lesssim$ v ~ 10^-3c. In addition, their mass is small, resulting in a long de Broglie wavelength and a high particle number density. Their phase space distribution contains many uncertainties, so they could give rise to either a coherent or noncoherent wave on the laboratory scale. In this paper, we demonstrated that a resonant cavity can enhance noncoherent axion-to-photon or dark photon-to-photon transitions, and the resulting power is the same as in the coherence case. The classical picture explanation is that a cavity can resonant with multiple different sources simultaneously. This aligns with the quantum perspective, where the cavity boosts dark matter particles transitioning into photons similarly to the Purcell effect. This effect increases the density of states near resonance, regardless of the coherence nature of dark matter. Certainly, the induced microwave signals in a cavity are also non-coherent, and in such case, a single-photon readout may be required.

The probabilities of forming an α-particle at the surface of heavy nuclei (spectroscopic factors) in the states of different angular momenta are calculated within the dinuclear system (DNS) approach. It is shown that this dependence is determined not only by the energies of the excited states of the daughter nucleus, as is suggested by the Boltzmann distribution, but also by its quadrupole and octupole deformation parameters. If the daughter nucleus is almost spherical, in the course of α-decay, it is predominantly populated in the ground state, whereas the population of other yrast states is strongly suppressed. If the daughter nucleus possesses quadrupole deformation but negligible octupole deformation, the states with even angular momenta are primarily populated. To populate the states with odd angular momenta, the daughter nucleus should be octupole deformed. The dependence of spectroscopic factors on the angular momentum of the daughter nucleus was calculated for actinide nuclei ^222-228Ra, ^222-232Th, ^226-236U, and ^234-242Pu. The results obtained will be useful in future studies on the fine structure of α-decay.

In the present work, based on the Wentzel-Kramers-Brillouin approximation and Bohr-Sommerfeld quantization condition, we extend a phenomenological modified harmonic oscillator potential model proposed by Bayrak [J. Phys. G 47: 025102, 2020] to systematically investigate the favored proton radioactivity by considering the spectroscopic factors S_p from the relativistic mean-field theory and the Bardeen-Cooper-Schrieffer method. Calculations show good agreement with experimental data within a factor of 2.7. Furthermore, employing this model, we predict the proton radioactivity half-lives of potential candidates that are energetically allowed or observed but not yet quantified in the latest atomic mass excess NUBASE2020. For comparison, the one-parameter model [Commun. Theor. Phys. 74: 115302, 2022] and the universal decay law [Phys. Rev. C 85: 011303, 2012] are also employed. All the corresponding predictions are consistent with each other. In addition, the reliability of our predictions is further confirmed by comparing the simple formula proposed by Delion et al [Phys. Rev. Lett. 96: 072501, 2006] and the new Geiger-Nuttall law put forward by Chen et al [Eur. Phys. J. A 55: 214, 2019].

A physics-informed neural network (PINN) is built to solve the nucleonic Dirac equation. The PINN employs the residual of the Dirac equation as the objective function instead of the variation of the energy expectation value, thereby avoiding the variational collapse problem. By integrating the automatic differentiation techniques, the PINN also overcomes the Fermion doubling problem. A constraint term in the loss function of the PINN is designed to avoid trivial solutions and an orthogonality constraint term is used to search for the excited states. The performance of the unsupervised PINN is evaluated by solving the orbitals below the Fermi surface of ¹⁶O and ²⁰⁸Pb in the Dirac Woods-Saxon (WS) potential. Compared to the results obtained by the traditional shooting method, obtained energies have relative errors on the order of 10^-3 and the root-mean-square errors of the corresponding wave functions are also on the order of 10^-3.

In this study, we explore the recently proposed f(R, A) gravity, a novel extension of modified gravity theories, where R represents the Ricci scalar and A denotes the anticurvature scalar. The addition of anticurvature term might play a role in softening or avoiding singularities, offering smoother transitions in regions of high curvature, such as near black holes or during cosmic inflation (Amendol et al 2020 Phys. Lett. B 811 135923). We also incorporate well-established cosmological bouncing scenarios, including the symmetric bounce, oscillatory bounce, matter bounce, little rip, and super bounce, to examine their implications within the framework of underlying gravity theory. In this context, we investigate some cosmic and thermodynamic aspects of flat FRW universe. We analyze the effective equation of state parameter ω_eff, which exhibits a transition from quintessence to phantom regimes across different bouncing cosmologies. The stability of the models is examined through the squared speed of sound parameter ${v}_{s}^{2}$, confirming stability in certain bouncing scenarios. The validity of the generalized second law of thermodynamics is verified by ensuring the positivity of total entropy production ${\dot{S}}_{\mathrm{tot}}$. Additionally, the ${\omega }_{\mathrm{eff}}-{\omega }_{\mathrm{eff}}^{{\prime} }$ plane exhibits the thawing as well as the freezing regions. Our findings demonstrate that the chosen bouncing models provide viable cosmic and thermodynamic behavior, supporting their relevance in modified gravity theories.

This study presents an analysis of cosmological parameters, focusing on resolving the Hubble tension and constraining neutrino masses within a coupled quintom model. By utilizing datasets from the cosmic microwave background (CMB), Pantheon+Analysis, cosmic chronometers, baryon acoustic oscillations, and CMB Lensing, we explore the interplay between cosmological parameters and observational constraints. The model effectively reduces the Hubble tension, achieving a consistency in H₀ measurements of 1.37σ and 1.24σ for the CMB+ALL dataset for Planck 2018 and R22, respectively. Additionally, the study refines constraints on the total mass of neutrinos (${{\rm{\Sigma }}m}_{\nu }$), with a finding of 0.115 eV for the CMB+ALL dataset. The analysis examines the effective equation of state parameter (w_eff), indicating a transition towards a Universe dominated by exotic energy forms. The combined datasets refine w_eff to -1.02 ± 0.018, underscoring the importance of multi-dataset integration in understanding dark energy dynamics. Furthermore, the interaction constant β between the quintom scalar field and neutrinos is constrained to 0.65 ± 0.12 for the CMB+ALL dataset. The potential parameters λ_σ = -2.09 ± 0.082 and λ_Φ = 2.43 ± 0.12 are also determined, providing insights into the quintom model's implications for cosmological dynamics. This study offers compelling evidence for the coupled quintom model's capability to resolve the Hubble tension and refine constraints on neutrino properties, enhancing our understanding of the Universe's evolution.

Stimulated radiation and gravitational waves (GWs) are two of the most important predictions made by Albert Einstein. In this work, we demonstrate that stimulated GW radiation can occur within gravitational atoms, which consist of Kerr black holes and the surrounding boson clouds formed through superradiance. The presence of GWs induces mixing between different states of the gravitational atoms, leading to resonant transitions between two states when the GW wavenumber closely matches the energy difference. Consequently, the energy and angular momentum released from these transitions lead to the amplification of GWs, resulting in an exponential increase in the transition rate. Remarkably, the transitions complete within a period much shorter than the lifetime of the cloud. These stimulated transitions give rise to a novel GW signal that is strong and directed, distinguished from the previously predicted continuous GWs originating from clouds of ultralight bosons.

Using a model-independent Gaussian process (GP) method to reconstruct the dimensionless luminosity distance D and its derivatives, we derive the evolution of the dimensionless Hubble parameter E, the deceleration parameter q, and the state parameter w of dark energy. We utilize the PantheonPlus, SH0ES, and Gamma Ray Burst (GRB) data to derive the dimensionless luminosity distance D. Additionally, we employ observational H(z) data (OHD) and baryon acoustic oscillations (BAO) from the Dark Energy Spectroscopic Instrument (DESI) Data Release 2 (DR2) to obtain the first derivative of the dimensionless luminosity distance ${D}^{{\prime} }$. To obtain the reconstructed D and ${D}^{{\prime} }$, we utilize the fiducial value from each dataset, with particular emphasis on the varying H₀. According to the reconstruction results obtained from PantheonPlus+SH0ES+GRB+OHD and PantheonPlus+SH0ES+GRB+OHD+DESI data, we find that E is consistent with the predictions of the $\Lambda$CDM model at a 2σ confidence level within the redshift range of z < 2. However, the reconstruction results for q exhibit deviations from the $\Lambda$CDM model in the range of z < 0.3. Furthermore, we observe that the mean value of w exhibits evolving behavior, transiting from w < -1 to w > -1 around ${z}_{{\rm{wt}}}=0.46{4}_{-0.120}^{+0.235}$. Combining data from DESI DR2 can slightly enhance the accuracy of our constraints.

In this paper, we investigate the thermodynamic properties and geometries of phantom (A)dS F(R) black holes in the presence of recently proposed generalized entropy. For this purpose, we evaluate the heat capacity, Helmholtz free energy, Gibbs free energy, compressibility factor Z and the isothermal compressibility (κ_T) to analyze the local and global stability of this black hole. We also analyze the thermal geometries of this black hole, which provide useful insights. Furthermore, we present isotherms on the P-V diagram, illustrating phase behavior. It is interesting to mention here that generalized entropy provides a significant and useful impact on the results of thermal analysis of the aforementioned black holes.

This article investigates the pseudo phase transition behavior of the six-state clock model on two-dimensional finite-size lattices. By employing the Wang-Landau sampling method and microcanonical inflection-point analysis, we identified two phase transition points and classified both as continuous transitions within the microcanonical framework. Using Metropolis sampling and canonical ensemble analysis, we verified the accuracy of the transition points obtained from the microcanonical approach and further pinpointed the location of a fourth-order dependent transition with high accuracy. Moreover, the fourth-order dependent transition points extracted from two canonical order parameters——the average cluster perimeter and the ${M}_{{{\mathbb{Z}}}_{6}}$ symmetry——are in excellent agreement and consistently reinforce each other. Through a detailed analysis of the ${M}_{{{\mathbb{Z}}}_{6}}$ symmetry, we further demonstrate that the position of this fourth-order dependent transition may function as a critical transition warning indicator for both primary phase transitions in the system.

The Wiedemann-Franz (WF) law, a foundational principle in condensed matter physics, posits a direct proportionality between the electronic contributions to thermal and electrical conductivity. However, recent experimental observations, particularly in materials like vanadium dioxide (VO₂), have revealed significant violations of this law. Furthermore, a growing body of evidence indicates its inapplicability under cryogenic conditions, highlighting the need for a more comprehensive theoretical framework. This study addresses this discrepancy by deriving a generalized WF law. Beginning with the thermodynamic potential of a relativistic degenerate electron gas and electron density functions, we employ a swallowtail catastrophe model grounded in structural stability principles, in conjunction with non-dimensional analysis. The resulting formulation yields a general WF law that correctly satisfies the boundary conditions at both cryogenic and infinite-temperature limits. Our findings reveal that the relationship between thermal and electrical conductivity is fundamentally nonlinear, intrinsically dependent on the material's relaxation time and chemical potential. To validate our framework, we have applied the derived law to calculate the thermal conductivity of VO₂, achieving excellent agreement with previously reported experimental data. This generalized WF law provides a robust theoretical tool for analyzing electron transport phenomena and holds significant potential for investigating phase transitions in metals and superconductors.

A primitive problem of predicting effective properties of composites is open boundary conditions. In this paper, Eshelby's transformation field method (TFM) is developed to solve the open boundary problem of two-phase composites having an arbitrary geometry of inclusion. The inhomogenous transformation fields are introduced in the composite system to cope with the complex interface boundary-value problem. Furthermore, the open boundary problem is solved by a Hermite polynomial, which is used to express the transformation fields and the perturbation fields. As an example, the formulas of calculating effective dielectric property of two-dimensional isotropic dielectric composites having open boundary conditions are derived by TFM. The validity is verified by comparing the effective responses estimated by TFM with the exact solutions of the dilute limit, and good agreements are obtained. The results show that TFM is valid to solve the open boundary problem of composites having complex geometric inclusions.

Leveraging an optimized transfer matrix strategy, we numerically investigated the effect of δ-doping on the transmission probability, conductance, and magnetoresistance ratio in a semiconductor 2DEG heterostructure modulated by two overlapping magnetic barriers. High-precision computations revealed the dependence of the peak magnetoresistance ratio and its Fermi energy position on the weight and position of the δ-doping. The results demonstrate that the performance of giant magnetoresistance (GMR) devices can be effectively tuned by optimizing both the position and strength of δ-doping. By comparing our results with prior calculations and theoretical predictions, we find strong agreement with theoretical expectations, but also significant deviations from earlier studies due to critical numerical inaccuracies in their methodologies. By addressing these discrepancies, our optimized approach provides a fast and versatile framework for analyzing spin-dependent transport in complex magnetic-electric hybrid systems.