The main focus of this paper is to address a generalized (2+1)-dimensional Hirota bilinear equation utilizing the bilinear neural network method. The paper presents the periodic solutions through a single-layer model of [3-4-1], followed by breather, lump and their interaction solutions by using double-layer models of [3-3-2-1] and [3-3-3-1], respectively. A significant innovation introduced in this work is the computation of periodic cross-rational solutions through the design of a novel [3-(2+2)-4-1] model, where a specific hidden layer is partitioned into two segments for subsequent operations. Three-dimensional and density figures of the solutions are given alongside an analysis of the dynamics of these solutions.
The aim of this paper is to study an extended modified Korteweg–de Vries–Calogero–Bogoyavlenskii–Schiff (mKdV-CBS) equation and present its Lax pair with a spectral parameter. Meanwhile, a Miura transformation is explored, which reveals the relationship between solutions of the extended mKdV-CBS equation and the extended (2+1)-dimensional Korteweg–de Vries (KdV) equation. On the basis of the obtained Lax pair and the existing research results, the Darboux transformation is derived, which plays a crucial role in presenting soliton solutions. In addition, soliton molecules are given by the velocity resonance mechanism.
We investigate dark solitons lying on elliptic function background in the defocusing Hirota equation with third-order dispersion and self-steepening terms. By means of the modified squared wavefunction method, we obtain the Jacobi’s elliptic solution of the defocusing Hirota equation, and solve the related linear matrix eigenvalue problem on elliptic function background. The elliptic N-dark soliton solution in terms of theta functions is constructed by the Darboux transformation and limit technique. The asymptotic dynamical behaviors for the elliptic N-dark soliton solution as t → ± ∞ are studied. Through numerical plots of the elliptic one-, two- and three-dark solitons, the amplification effect on the velocity of elliptic dark solitons, and the compression effect on the soliton spatiotemporal distributions produced by the third-order dispersion and self-steepening terms are discussed.
New diverse enormous soliton solutions to the Gross–Pitaevskii equation, which describes the dynamics of two dark solitons in a polarization condensate under non-resonant pumping, have been constructed for the first time by using two different schemes. The two schemes utilized are the generalized Kudryashov scheme and the (G’/G)-expansion scheme. Throughout these two suggested schemes we construct new diverse forms solutions that include dark, bright-shaped soliton solutions, combined bright-shaped, dark-shaped soliton solutions, hyperbolic function soliton solutions, singular-shaped soliton solutions and other rational soliton solutions. The two 2D and 3D figure designs have been configured using the Mathematica program. In addition, the Haar wavelet numerical scheme has been applied to construct the identical numerical behavior for all soliton solutions achieved by the two suggested schemes to show the existing similarity between the soliton solutions and numerical solutions.
In this study we theoretically demonstrate ultrahigh-resolution two-dimensional atomic localization within a three-level λ-type atomic medium via superposition of asymmetric and symmetric standing wave fields. Our analysis provides an understanding of the precise spatial localization of atomic positions at the atomic level, utilizing advanced theoretical approaches and principles of quantum mechanics. The dynamical behavior of a three-level atomic system is thoroughly analyzed using the density matrix formalism within the realm of quantum mechanics. A theoretical approach is constructed to describe the interaction between the system and external fields, specifically a control field and a probe field. The absorption spectrum of the probe field is thoroughly examined to clarify the spatial localization of the atom within the proposed configuration. A theoretical investigation found that symmetric and asymmetric superposition phenomena significantly influence the localized peaks within a two-dimensional spatial domain. Specifically, the emergence of one and two sharp localized peaks was observed within a one-wavelength domain. We observed notable influences of the intensity of the control field, probe field detuning and decay rates on atomic localization. Ultimately, we have achieved an unprecedented level of ultrahigh resolution and precision in localizing an atom within an area smaller than λ/35 × λ/35. These findings hold promise for potential applications in fields such as Bose–Einstein condensation, nanolithography, laser cooling, trapping of neutral atoms and the measurement of center-of-mass wave functions.
Since the concept of quantum information masking was proposed by Modi et al (2018 Phys. Rev. Lett. 120, 230 501), many interesting and significant results have been reported, both theoretically and experimentally. However, designing a quantum information masker is not an easy task, especially for larger systems. In this paper, we propose a variational quantum algorithm to resolve this problem. Specifically, our algorithm is a hybrid quantum–classical model, where the quantum device with adjustable parameters tries to mask quantum information and the classical device evaluates the performance of the quantum device and optimizes its parameters. After optimization, the quantum device behaves as an optimal masker. The loss value during optimization can be used to characterize the performance of the masker. In particular, if the loss value converges to zero, we obtain a perfect masker that completely masks the quantum information generated by the quantum information source, otherwise, the perfect masker does not exist and the subsystems always contain the original information. Nevertheless, these resulting maskers are still optimal. Quantum parallelism is utilized to reduce quantum state preparations and measurements. Our study paves the way for wide application of quantum information masking, and some of the techniques used in this study may have potential applications in quantum information processing.
The fusion excitation functions for 12 colliding systems with 96 ≤ Z1Z2 ≤ 608 are analyzed using coupled-channel (CC) calculations based on the M3Y double-folding (DF) potential supplemented with a repulsive potential that takes into account the incompressibility of the nuclear matter. We also applied the polarization effects of hot nuclear matter (PEHNM) on the calculations of the bare nucleus–-nucleus interaction potential within the framework of the modified density-dependent Seyler–Blanchard (SB) approach in the T2 approximation. Our results reveal that we obtain a nice description of the experimental data of different fusion systems when we use the present theoretical approach to calculate the energy-dependent values of the fusion cross sections. In this paper, the influence of the PEHNM on the surface diffuseness parameter of the Woods–Saxon (WS) potential is also studied. In order to reach this goal, we extract the corresponding values of this parameter based on the modified form of the DF potential (M3Y+Repulsion+polarization). We find that the extracted values are located in a range between a = 0.61 and 0.80 fm at different incident energies. It seems that the polarization effects of hot nuclear matter play a key role in describing the abnormally large values of the nuclear potential diffusenesses in the heavy-ion fusion reactions. Additionally, the regular decreasing trend for the diffuseness parameter of the nucleus–nucleus potential with the increase in the bombarding energies is also observed.
The β-decay properties of 67−80As nuclei have been investigated within the framework of the proton–neutron quasi-particle random phase approximation (pn-QRPA) model. The nuclear deformation obtained from the finite range droplet model is used as an input parameter in the pn-QRPA model for the analysis of β-decay properties including Gamow–Teller strength distributions, log ft, β-decay half-lives and stellar β± decay rates. The predicted log ft values were fairly consistent with the observed data. The computed β-decay half-lives matched the measured values by a factor of 10. The stellar rates were compared with the shell model outcomes. At high densities and temperatures, the β+ and electron capture rates had a finite contribution. However, the β− and positron capture rates are only significant at high temperatures and low densities. The pn-QRPA rates outperformed the shell model rates by a factor of 22 or more.
The transverse-traceless gauge condition is an important concept in the theory of gravitational waves. It is well known that a vacuum is one of the key conditions to guarantee the existence of the transverse-traceless gauge. Although it is thin, the interstellar medium is ubiquitous in the Universe. Therefore, it is important to understand the concept of gravitational waves when matter is presented. Bondi–Metzner–Sachs theory has solved the gauge problem related to gravitational waves. But it does not help with cases when the gravitational wave propagates in matter. This paper discusses possible extensions of the transverse-traceless gauge condition to Minkowski perturbation with matter presented.
In this paper we consider a static spherically symmetric black hole (BH) embedded in a Dehnen-(1, 4, 0)-type dark matter (DM) halo in the presence of a cloud string. We examine and present data on how the core density of the DM halo parameter and the cloud string parameter affect BH attributes such as quasinormal modes (QNMs) and shadow cast. To do this, we first look into the effective potential of perturbation equations for three types of perturbation fields with different spins: massless scalar field, electromagnetic field and gravitational field. Then, using the sixth-order Wentzel–Kramers–Brillouin approximation, we examine QNMs of the BH disturbed by the three fields and derive quasinormal frequencies. The changes in QNM versus the core density parameter and the cloud string parameter for three disturbances are explored. We also investigate how the core density and the cloud string parameter affect the photon sphere and shadow radius. Interestingly, the study shows that the influence of Dehnen-type DM and cloud strings increases both the photon sphere and the shadow radius. Finally, we employ observational data from Sgr A⋆ and M87⋆ to set limitations on the BH parameters.
In this work, we consider the collapse of a ${\mathbb{D}}$-dimensional sphere in the framework of a higher-dimensional spherically symmetric space-time in which the gravitational action chosen is claimed to be somehow linked to the ${\mathbb{D}}$-dimensional modified term. This work investigates the criteria for the dynamical instability of anisotropic relativistic sphere systems with ${\mathbb{D}}$-dimensional modified gravity. The certain conditions are applied that lead to the collapse equation and their effects on adiabatic index Γ in both Newtonian (N) and Post-Newtonian (PN) regimes by using a perturbation scheme. The study explores that the Γ plays a crucial role in determining the degree of dynamical instability. This index characterizes the fluid’s stiffness and has a significant impact on defining the ranges of instability. This systematic investigation demonstrates the influence of various material properties such as anisotropic pressure, kinematic quantities, mass function, ${\mathbb{D}}$-dimensional modified gravity parameters, and the radial profile of energy density on the instability of considered structures during their evolution. This work also displays the dynamical behavior of spherically symmetric fluid configuration via graphical approaches.
This article primarily establishes a two-soliton system and employs the Lewis–Riesenfeld invariant inverse control method to achieve shortcuts to adiabaticity (STA) technology. We study an atomic soliton Josephson junctions (SJJs) device and subsequently compare and analyze it with atomic bosonic Josephson junctions. Moreover, we use higher-order expressions of the auxiliary equations to optimize the results and weaken the detrimental effect of the sloshing amplitude. We find that in the adiabatic shortcut evolution of two systems with time-containing tunnelling rates, the SJJs system is more robust over a rather short time evolution. In comparison with linear ramping, the STA technique is easier to achieve with the precise modulation of the quantum state in the SJJs system.
Understanding neural dynamics is a central topic in machine learning, non-linear physics, and neuroscience. However, the dynamics are non-linear, stochastic and particularly non-gradient, i.e., the driving force cannot be written as the gradient of a potential. These features make analytic studies very challenging. The common tool is the path integral approach or dynamical mean-field theory. Still, the drawback is that one has to solve the integro-differential or dynamical mean-field equations, which is computationally expensive and has no closed-form solutions in general. From the associated Fokker–Planck equation, the steady-state solution is generally unknown. Here, we treat searching for the fixed points as an optimization problem, and construct an approximate potential related to the speed of the dynamics, and find that searching for the ground state of this potential is equivalent to running approximate stochastic gradient dynamics or Langevin dynamics. Only in the zero temperature limit, can the distribution of the original fixed points be achieved. The resultant stationary state of the dynamics exactly follows the canonical Boltzmann measure. Within this framework, the quenched disorder intrinsic in the neural networks can be averaged out by applying the replica method, which leads naturally to order parameters for the non-equilibrium steady states. Our theory reproduces the well-known result of edge-of-chaos. Furthermore, the order parameters characterizing the continuous transition are derived, and the order parameters are explained as fluctuations and responses of the steady states. Our method thus opens the door to analytically studying the fixed-point landscape of the deterministic or stochastic high dimensional dynamics.
Active matter exhibits collective motions at various scales. Geometric confinement has been identified as an effective way to control and manipulate active fluids, with much attention given to external factors. However, the impact of the inherent properties of active particles on collective motion under confined conditions remains elusive. Here, we use a highly tunable active nematics model to study active systems under confinement, focusing on the effect of the self-driven speed of active particles. We identify three distinct states characterized by unique particle and flow fields within confined active nematic systems, among which circular rotation emerges as a collective motion involving rotational movement in both particle and flow fields. The theoretical phase diagram shows that increasing the self-driven speed of active particles significantly enhances the region of the circular rotation state and improves its stability. Our results provide insights into the formation of high quality vortices in confined active nematic systems.
Kármán vortex street not only exists in nature, but also widely appears in engineering practice, which is of great significance for understanding superfluid. Parity-time (PT) symmetric potential provides a good platform for the study of Kármán vortex streets. In this paper, different patterns of vortex shedding formed behind PT symmetric potential in Bose–Einstein condensate (BEC) are simulated numerically. Kármán vortex streets and others are discovered to emerge in the wake of a moving obstacle with appropriate parameters. Compared with BEC without PT symmetric potential, the frequency and amplitude of the drag force are more complex. The parametric regions of the combined modes are scattered around the Kármán vortex street. Numerical simulations indicate that the imaginary part of the PT symmetric potential affects the vortex structure patterns. Finally, we proposed an experimental protocol that may observe a Kármán vortex street.
We conduct a dynamical Gutzwiller mean-field study of interacting bosons on a four-leg ladder, subject to a uniform flux. The ground states dependent on the magnetic flux and kinetic tunneling strength are explored. Consequently, we identify the super-vortical lattice, as well as the inner-Meissner phase, which presents Meissner currents just along the intimal legs within the flux ladder. The staggered-current phase is also allowed, with its formation condition altered because of the four-leg construction. The number of legs on the flux ladder can make an effect.
In this paper, a tunable metamaterial absorber based on a Dirac semimetal is proposed. It consists of three different structures, from top to bottom, namely a double semicircular Dirac semimetal resonator, a silicon dioxide substrate and a continuous vanadium dioxide (VO2) reflector layer. When the Fermi energy level of the Dirac semimetal is $10\,{\rm{meV}},$ the absorber absorbs more than 90% in the 39.06–84.76 THz range. Firstly, taking advantage of the tunability of the conductivity of the Dirac semimetal, dynamic tuning of the absorption frequency can be achieved by changing the Fermi energy level of the Dirac semimetal without the need to optimise the geometry and remanufacture the structure. Secondly, the structure has been improved by the addition of the phase change material VO2, resulting in a much higher absorption performance of the absorber. Since VO2 is a temperature-sensitive metal oxide with an insulating phase below the phase transition temperature (about 68 °C) and a metallic phase above the phase transition temperature, this paper also analyses the effect of VO2 on the absorptive performance at different temperatures, with the aim of further improving absorber performance.
