In this paper, the parameter-constrained long wave limit method is proposed to investigate the (2+1)-dimensional Korteweg–de Vries system. This method overcomes the limitation of the conventional approach caused by the special cross-term structure and enables the analytical construction of the lump and one-lump-$M$-stripe solutions. For $M = 1$ and $M = 2$, explicit formulas are presented and the corresponding dynamic behaviors are analyzed. The lump wave moves from the position determined by one polynomial function to another after collision, with only a phase shift. The two stripe waves exhibit either crossing or overtaking behavior. This work extends the applicability of the long wave limit method and deepens the understanding of elastic interaction in high-dimensional integrable systems.
The possibility of the existence of chirped coupled periodic waves in a two-mode optical fiber exhibiting self-steepening nonlinearity is shown. Derived nonlinear waves comprise coupled dn–dn-type and cn–cn-type periodic waves, thus illustrating the diversity of propagating nonlinearly chirped periodic waveforms in the bimodal fiber system. Also, the bright-dark soliton pair is obtained in the long-wave limit of these periodic waves. It is demonstrated that each of the two wave components exhibits a nonlinear chirp that is directly proportional to its intensity. We further show that the group velocity dispersion parameter enables one to control the amplitude and background of the chirp effectively. The periodic and localized wave solutions presented here are of particular interest in the study of the transmission properties of optical pulses due to their frequency chirping property and precise nature.
Existing research on relaxing the no-arbitrage assumption within the Black–Scholes framework remains relatively limited. To bridge the gap between this idealized assumption and the presence of arbitrage opportunities in real markets, we derive an option pricing model with endogenous stochastic arbitrage. This provides an analytical framework for characterizing localized fluctuations in option prices. Using empirical data on Nasdaq-100 E-mini futures options, we identify and characterize a general form of the arbitrage perturbation. We then apply the Lie symmetry method to the modified Black–Scholes equation and derive its Lie symmetry group and infinitesimal generators. Based on these infinitesimal generators, we derive invariants by solving the associated characteristic equations, from which the exact solutions are obtained. Finally, the numerical results show that, in the presence of localized price fluctuations, the proposed endogenous stochastic arbitrage model reduces pricing errors more effectively than the classic Black–Scholes model. This study not only extends option pricing analysis under non-equilibrium market conditions from the perspective of localized fluctuations, but also enriches the study of symmetry analysis and explicit solutions for modified Black–Scholes-type equations.
The variable-coefficient nonlinear Schrödinger equation is investigated via the Riemann–Hilbert problem (RHP) with arbitrary-order poles under zero boundary conditions. The asymptotic behavior, analyticity, and symmetry of the Jost solutions and scattering coefficients are derived. In the reflectionless case, the formulas of the soliton solutions corresponding to single and multiple higher-order poles are derived via the Laurent expansion of the RHP. The method transforms the solution process into solving linear algebraic equations, avoiding complicated calculations and directly yielding the expressions for higher-order pole solutions corresponding to scattering data with $N$ distinct poles. In addition, several special poles and their corresponding soliton solutions are presented explicitly, including one second-order pole, one third-order pole, two second-order poles, and other cases. The results verify that the associated Riemann–Hilbert approach is efficient for constructing higher-order localized solutions of integrable systems.
We compute holographic one-point functions for Wilson surfaces in the case of a toroidal surface operator. Compared to the cases of a planar or spherical surface operator, these one-point functions exhibit a more intricate dependence on the shape and position of both the surface and the local operators. Averaging over the moduli space of membranes dual to the surface operator plays a key role in the computations. We obtain both analytical and numerical results. The case of a cylindrical surface operator is also studied.
We study the long-time asymptotics of the coupled Sasa–Satsuma equation, a system with a $5\times5$ Lax pair whose rigorous analysis has remained open. Using the inverse scattering transform and the $\bar\partial$-steepest descent method, we prove soliton resolution for generic Schwartz-class initial data. Precise asymptotic formulas are obtained in five distinct spacetime regions: an oscillatory zone ($x \lt 0$, $|x/t| = \mathcal{O}(1)$) with $t^{-1/2}$ corrections, a soliton zone ($x \gt 0$, $|x/t| = \mathcal{O}(1)$) with $t^{-1}$ decay, a Painlevé zone ($|x/t^{1/3}| = \mathcal{O}(1)$) described by the classical Painlevé II equation, and two transition zones connecting them (detailed in the
In this paper, various localized wave solutions of the (2+1)-dimensional generalized nonlocal Fokas system are under investigation, through the combination of the bilinear method and long-wave limit technique. By using Hirota’s bilinear method and choosing appropriate parameters, single-periodic and two types of two-periodic wave solutions are obtained, and two-periodic waves are classified into two categories based on the positional relationships of the characteristic lines. The long-wave limit method is used to construct rational solutions, and we also analyze the dynamic characteristics of higher-order rogue waves. Furthermore, semi-rational solutions derived by the partial long-wave limit method include the following forms: (1) lumps on a dark soliton background, (2) lumps embedded in a periodic wave background, (3) a rogue wave on a periodic wave background, (4) a rogue wave on a line soliton background and (5) a rogue wave on the two parallel solitons background. The resulting solutions are helpful for analyzing the dynamic behavior of nonlinear waves.
Quantum battery charging in an optimized manner is of significance in quantum state engineering and technology. This paper presents an efficient scheme for rapidly charging a superconducting qutrit battery via shortcuts to adiabaticity. A qutrit battery of a superconducting quantum circuit having sufficient level anharmonicity is driven by two classical microwave fields, constituting an effective $\Lambda$-configuration interaction. Within the framework of invariant-based inverse engineering, the fast charging of the qutrit battery can be realized through suitably designing the Rabi frequencies without the restriction of adiabatic criterion. Numerical simulations showcase that high-efficiency charging could be obtained in the presence of noise decoherence and timing error. Thus the scheme could pave a feasible avenue to investigate qutrit battery charging in a fast and robust way in experiments.
In this paper, we study the transition form factors (TFFs) of the lightest pseudoscalar mesons, $\pi^0$, $\eta$, and $\eta^{^{\prime}}$, within the framework of resonance chiral theory. Our analysis is performed based on the data of time-like and space-like singly-virtual and space-like doubly-virtual form factors, as well as the relevant cross sections and latest invariant mass spectra of $e^+e^-$ pair for the process of $P\to\gamma e^+ e^-$. The TFFs of these pseudoscalars are obtained. Also, we evaluate their contributions to the light-by-light part of the anomalous magnetic moment of the muon. Our two fits give similar results, where the better fit (Fit-A) gives $a_\mu^{\pi^0 } = (61.6\,\pm\,1.8)\times10^{-11}$, $a_\mu^{\eta } = (15.2\pm1.7)\times10^{-11}$, $a_\mu^{\eta^{^{\prime}}} = (16.0\,\pm\,1.2)\times10^{-11}$, and the total contribution of neutral pseudoscalar meson poles is $a_\mu^{\pi^0+\eta+\eta^{^{\prime}}} = (92.8\pm2.9)\times10^{-11}$.
The current work investigates the elastic scattering of the weakly bound nucleus 6Li on the heavy, deformed target 232Th across an energy range of 26–44 MeV, employing both semi- and fully microscopic approaches. These approaches were performed with a particular focus on the breakup effects of 6Li’s low binding energy (1.47 MeV) on scattering dynamics. Pronounced breakup contributions were observed using cluster folding and energy-dependent (SPP2, S1Y, KH3, R3Y, CDM3Y6) as well as energy-independent (BNP) double-folding potentials. Furthermore, the presence of the breakup threshold anomaly is supported by a consistent imaginary potential near the Coulomb barrier. All tested potentials successfully reproduce the differential cross sections, exhibiting comparable energy-dependent trends in their parameters.
We investigate how the Hawking effect reshapes distinct quantum resources of Dirac fields in Schwarzschild spacetime beyond the single-mode approximation. By quantifying quantum entanglement and coherence using the negativity, the $l_1$-norm of coherence and the relative entropy of coherence, we observe a significant asymmetry in their response to gravitational effects. While the Hawking effect monotonically degrades entanglement and drives it toward a finite residual value, quantum coherence is instead monotonically amplified with increasing Hawking temperature, revealing the black hole as an effective decohering environment for nonlocal correlations but a coherence-enhancing mechanism for local superposition. Notably, we further find that under the influence of the Hawking effect, the maximally entangled state does not necessarily correspond to the largest initial negativity. In fact, its value may even be smaller than that of certain non-maximally entangled states. Our results demonstrate that gravity acts in a highly nonuniform manner on different facets of quantumness and highlight the necessity of resource-adapted state engineering for relativistic quantum information processing near the event horizon of the black hole.
The principal aim of this investigation is to ascertain novel theoretical solutions for charged traversable wormholes within the Rastall teleparallel gravity paradigm, with a particular emphasis on two distinct dark matter halo configurations. The Morris–Thorne framework offers a characterization of the wormhole structure, and under this geometry, the associated field equations are expressed via the torsion scalar governed by the anisotropic fluid. The subsequent analysis includes imposing a constant redshift function which permits us to build two distinct shape functions. We then assess whether these functions meet all essential requirements for a traversable wormhole and confirm that a spacetime bridge linking two asymptotically flat regions is successfully constructed. For these solutions to be theoretically possible, the null energy conditions must be violated, meaning exotic matter would have to be present. We also analyze several key properties to fully describe our solutions, such as the active gravitational mass, the quantity of exotic matter, the spatial geometry from embedding diagrams, and the pressure anisotropy. We show that the resulting wormhole configurations are theoretically valid, as they satisfy the essential criteria within the framework of non-conserved torsion-based gravity.
In the Einstein–Bardeen model coupled to a free complex scalar field, the introduction of the scalar field prevents the formation of an event horizon. When the magnetic charge $q$ exceeds a certain critical value, a frozen Bardeen–Boson star can be obtained with the frequency $\omega \rightarrow 0$. In this paper, we extend this model by including a charged scalar field and obtain two types of solutions: the small $q$ solution and the large $q$ solution. For the small $q$ solution, we find that there exists a maximum value for the charge $q$; the introduction of the charge makes it possible to obtain frozen star solutions without requiring the frequency to approach zero. For the large $q$ solution, the charge can tend toward infinity.
The Photonic spin Hall effect (PSHE) offers fundamental insights into spin–orbit interactions of light, yet its control over compact, tunable platforms remains a challenge. Here, we investigate the PSHE in a solid-state platform of $N$-coupled quantum dots (CQDs), focusing on both the linear absorption and Kerr nonlinear regimes. On this platform, an external electric field controls electron tunneling between CQDs, resulting in multiple tunneling-induced transparency windows. We report a giant enhancement of the Kerr nonlinearity, achieving orders-of-magnitude increases while suppressing linear absorption—a domain that is favorable for low-power nonlinear photonics. Exploiting this, we demonstrate that the PSHE shift can be drastically enhanced and controlled by tuning the excited-state transition frequency and tunneling strengths, which significantly modify the Brewster angle. This active nonlinear control improves static nanostructures by combining the tunability of atomic systems with the functionality of an integrable quantum material. Our results establish $N$-CQDs as a viable platform for producing giant Kerr nonlinearity-driven PSHE, opening up new possibilities for tunable low-power spin–orbit light control in quantum photonics.
The formation of phonon band gaps is a fundamental feature of many periodic systems with internal structural asymmetry and plays an important role in lattice dynamics and wave propagation. Binary complex plasmas provide a controllable model system for investigating collective excitations under strongly coupled conditions. In this work the phonon band structure of one-dimensional binary complex plasma chains is studied using Langevin dynamics simulations with particular attention to the robustness of phonon band gaps under realistic plasma conditions. While ideal theoretical models predict a clear separation between acoustic and optical branches it remains unclear whether this feature can persist in the presence of thermal fluctuations and dissipation. The present results show that the phonon band gap survives beyond the ideal limit and exhibits systematic variations with particle and plasma parameters. In particular particle size is found to play a key role through its combined influence on particle inertia and electrostatic interactions. These results provide physical insight into collective excitations in strongly coupled systems and demonstrate that complex plasmas offer a useful platform for exploring tunable phononic behavior in ordered many body lattices.
Epitaxial growth is a process in which a crystalline layer is deposited on a crystalline substrate. In this study, we investigate the nonequilibrium epitaxial growth of two-dimensional active crystals on solid substrates using Langevin dynamics simulations of purely repulsive active Brownian particles. Driven by motility-induced phase separation, the crystallization process exhibits two distinct regimes: an initial layer-by-layer deposition and subsequent interfacial growth evolution. During the initial stage, the temporal evolution of the layer coverage ratio follows a logistic-type growth curve, which is quantitatively described by a kinetic flux balance model. During the steady-state phase, a fluctuating solid–gas interface with a stable average height is formed. It is characterized by an internal dense phase, which primarily consists of a hexagonal lattice, with local topological defects near the interface. While increasing the Péclet number accelerates the initial layer coverage rate, it decreases the steady-state interfacial height and increases the bulk density of the active solid phase. Our results demonstrate that particle self-propulsion can alter the crystallization process.
To investigate the impact of long-range temporal correlations on height distributions in the kinetic roughening of growing interfaces, we perform numerical simulations of two discrete growth models in the Kardar–Parisi–Zhang (KPZ) universality class, namely the ballistic deposition (BD) and restricted solid-on-solid (RSOS) models, both driven by long-range temporally correlated noise with exponent $\theta \in [0,0.4]$. Our numerical results indicate that, in the growth regime, there exists a critical threshold $\theta_\mathrm c \approx 0.2$ that separates two distinct regimes. For temporal correlation exponents $\theta \lt \theta_\mathrm{c}$, the height distributions of both the BD and RSOS models closely align with the Tracy–Widom (TW) distribution. However, when $\theta \gt \theta_\mathrm{c}$, height distributions indicate the emergence of a new universality class. Correspondingly, the skewness ($S$) and kurtosis ($K$) of height distributions for both models are similarly affected by temporal correlations, and these quantities remain stable below $\theta_\mathrm c$ but increase significantly above it. In the saturation regime, the height-increment distributions of both the standard BD and RSOS models converge to the Baik–Rains (BR) distribution. Moreover, with increasing $\theta$, the $S$ and $K$ of both models exhibit a common nonmonotonic trend, first decreasing gradually and then increasing sharply. In the absence of the height transformation $h \to -h$, the differences observed between the two discrete growth models indicate that the nontrivial features of height distributions emerge from the interplay between nonlinear growth mechanisms and temporally correlated noise. We further compare the microscopic mechanisms of these growth models to elucidate how the influence of long-range temporal correlations couples with the intrinsic growth rules.
This paper systematically explores the third-order nonlinear optical properties and modulation mechanisms of a spherical quantum dot system confined by a Mie-type potential. We analytically solve the Schrödinger equation with Nikiforov–Uvarov method based on effective mass approximation to obtain the eigenenergies and wave function of the system. Subsequently, key third-order nonlinear optical parameters, including the third-harmonic generation (THG) coefficient, total optical absorption coefficients, and refractive index changes, are derived via the density matrix formalism. The results indicate that the nonlinear optical responses strongly depend on the geometric dimensions and the microscopic confinement parameters. By adjusting these parameters, effective control over the THG coefficient can be achieved. Furthermore, this study reveals the significant modulation effects of environmental factors. The synergistic influence of quantum dot size, confinement potential, and environmental interactions is systematically analyzed, providing a theoretical basis for designing high-performance nonlinear optical devices based on quantum dots.
Despite the challenges associated with their experimental synthesis, chalcogenide perovskites have emerged as viable alternatives to conventional halide perovskites, offering a promising Pb-free pathway for energy applications. In this work, the structural, electronic, optical, and thermoelectric properties of BaHfSe3 are systematically investigated using first-principles calculations within the framework of density functional theory combined with ab initio molecular dynamics (AIMD). The orthorhombic Pnma phase is found to be thermally stable up to 900 K based on AIMD simulations, with no evidence of structural degradation or phase transition under the simulated conditions. Electronic structure analysis using the Perdew–Burke–Ernzerhof functional reveals an indirect fundamental band gap of 0.39 eV (R → Γ), while HSE calculations increase the gap to 0.89 eV. The calculated optical response shows strong inter-band transitions between 2–4 eV and a high absorption coefficient exceeding 105 cm−1, highlighting the suitability of the material for optoelectronic applications. Thermoelectric transport properties, evaluated within the constant relaxation time approximation, indicate a peak Seebeck coefficient of approximately 305 µV K−1 near 400 K, accompanied by a thermally activated increase in electrical conductivity (σ/τ) and relatively low electronic thermal conductivity (Ke/τ < 3 W m−1 K−1). These features collectively result in a favorable power factor in the intermediate temperature range. Furthermore, the temperature-dependent heat capacity follows Debye-like behavior, suggesting weak anharmonic lattice performance and stable lattice dynamics.
$A = 6$ nuclei provide unique systems with two particles outside the tightly-bound $^4$He core. In the present work, we investigate $A = 6\,\,^{6}$He, $ ^{6}$Be and $ ^{6}$Li nuclei using $\textit{ab initio}$ Gamow many-body perturbation theory with a N$^3$LO nucleon–nucleon interaction. The complex-momentum Berggren basis provides a good framework to treat bound, resonance and continuum states on equal footing. The calculation well reproduces the two-neutron halo structure of $ ^{6}$He with a significantly large neutron radius. To investigate the spatial distribution of the two valence neutrons relative to the $ ^{4}$He core, we calculate two-body correlation density. Our calculations indicate that the two neutrons prefer a dineutron configuration over a cigar-like configuration. The ground states of $ ^{6}$Be and $ ^{6}$He belong to the isospin $T = 1$ triplet, and exhibit similar configurations. However, due to the Coulomb repulsion, the diproton configuration in $ ^{6}$Be (the mirror partner of $ ^{6}$He) is less prominent.
