In this paper, the modulation instability (MI), rogue waves (RWs) and conservation laws of the coupled higher-order nonlinear Schrödinger equation are investigated. According to MI and the 2 × 2 Lax pair, Darboux-dressing transformation with an asymptotic expansion method, the existence and properties of the one-, second-, and third-order RWs for the higher-order nonlinear Schrödinger equation are

A lattice model for strongly interacting electrons motivated by a rank-3 tensor model provides a tool for understanding the pairing mechanism of high-temperature superconductivity. This Sachdev–Ye–Kitaev-like model describes the strange metal phase in the cuprate high temperature superconductors. Our calculation indicates that the superconducting gap ratio in this model is higher than the ratio in

Hopfield neural networks on scale-free networks display the power law relation between the stability of patterns and the number of patterns. The stability is measured by the overlap between the output state and the stored pattern which is presented to a neural network. In simulations the overlap declines to a constant by a power law decay. Here we provide the explanation for the power law behavior

In this paper, we have framed bouncing cosmological model of the Universe in the presence of general relativistic hydrodynamics in an extended theory of gravity. The metric assumed here is the flat Friedmann–Robertson–Walker space–time and the stress energy tensor is of perfect fluid. Since general relativity (GR) has certain issues with late time cosmic speed up phenomena, here we have introduced

A scheme for remote weak-signal sensors is proposed, in which a coupled-resonator optical waveguide (CROW), as a transmitter, couples to a hybrid optomechanical cavity and an observing cavity at its two ends. Non-Markovian theory is employed to study the weak-force sensor by treating the CROW as a non-Markovian reservoir of cavity fields. The dissipationless bound states in the non-Markovian regime

We study the entanglement dynamics of two atoms coupled to their own Jaynes–Cummings cavities in single-excitation space. Here, we use concurrence to measure atomic entanglement, and consider the Bell-like states to be initial states. Our analysis suggests that collapse and revival take place in entanglement dynamics. The physical mechanism behind entanglement dynamics is periodic information and energy

We investigate the average coherence with respect to a complete set of complementary measurements. By using a Wigner–Yanase skew information-based coherence measure introduced in Luo and Sun (2017 Phys. Rev. A 96 , 022130), we evaluate the average coherence of a state with respect to any complete set of mutually unbiased measurements and general symmetric informationally complete measurements, respectively

In order to clarify the edge and interface effect on the adhesion energy between graphene (Gr) and its substrate, a theoretical model is proposed to study the interaction and strain distribution of Gr/Si system in terms of continuum medium mechanics and nanothermodynamics. We find that the interface separation and adhesion energy are determined by the thickness of Gr and substrate. The disturbed interaction

Many intracellular transports are performed by multiple molecular motors in a cooperative manner. Here, we use stochastic simulations to study the cooperative transport by multiple kinesin motors, focusing mainly on effects of the form of unbinding rate versus force and the rebinding rate of single motors on the cooperative transport. We consider two forms of the unbinding rate. One is the symmetric

Using a Monte Carlo simulation and the single histogram reweighting technique, we study the critical behaviors and phase transitions of the Baxter–Wu (BW) model on a two-layer triangular lattice with Ising-type interlayer couplings. Via the finite-size analysis, we obtain the transition temperatures and critical exponents at repulsive and attractive interlayer couplings. The data for the repulsive

Ca 2+ plays an important role in cell signal transduction. Its intracellular propagation is the most basic process of Ca 2+ signaling, such as calcium wave and double messenger system. In this work, with both numerical simulation and mean field ansatz, the three-dimensional probability distribution of Ca 2+ , which is read out by phosphorylation, is studied in two scenarios with boundaries. The coverage

In this paper, propagation characteristics of electromagnetic electron cyclotron (EMEC) waves based on kappa-Maxwellian distribution have been investigated to invoke the interplay of the electric field parallel to the Earth’s magnetic field and auroral trapped electrons. The dispersion relation for EMEC waves in kappa-Maxwellian distributed plasma has been derived using the contribution of the parallel

We investigate the quantum dynamics of two defect centers in solids, which are coupled by vacuum-induced dipole–dipole interactions. When the interaction between defects and phonons is taken into account, the two coupled electron–phonon systems make up two equivalent multilevel atoms. By making Born–Markov and rotating wave approximations, we derive a master equation describing the dynamics of the

We investigate a continuous Heisenberg spin chain equation which models the local magnetization in ferromagnet with time- and site-dependent inhomogeneous bilinear interaction and time-dependent spin-transfer torque. By establishing the gauge equivalence between the spin chain equation and an integrable generalized nonlinear Schrödinger equation, we present explicitly a novel nonautonomous magnetic

We study the sensitivity of energy eigenstates to small perturbation in quantum integrable and chaotic systems. It is shown that the distribution of rescaled components of perturbed states in unperturbed basis exhibits qualitative difference in these two types of systems: being close to the Gaussian form in quantum chaotic systems, while, far from the Gaussian form in integrable systems.

We have theoretically investigated two-dimensional atom localization using the absorption spectra of birefringence beams of light in a single wavelength domain. The atom localization is controlled and modified through tunneling effect in a conductive chiral atomic medium with absorption spectra of birefringent beams. The significant localization peaks are investigated in the left and right circularly

Despite some empirical successes for solving nonlinear evolution equations using deep learning, there are several unresolved issues. First, it could not uncover the dynamical behaviors of some equations where highly nonlinear source terms are included very well. Second, the gradient exploding and vanishing problems often occur for the traditional feedforward neural networks. In this paper, we propose

Because of its unique optoelectronic properties, people have studied the characteristics of polarons in various quantum well (QW) models. Among them, the asymmetrical semi-exponential QW (ASEQW) is a new model for studying the structure of QWs in recent years. It is of great significance to study the influences of the impurity and anisotropic parabolic confinement potential (APCP) on the crystal’s

The manuscript attempts to explore the periodicity in the distribution of galaxies in the recently reported Saraswati supercluster and the Stripe 82 region containing it as an example. The report of 120 Mpc periodicity in the Abell galaxy clusters by power spectrum analysis is the motivation behind the study. The power spectral analysis across the central part of the Stripe 82 region shows a periodic

Gravity and thermal energy are universal phenomena which compete over the stabilization of astrophysical systems. The former induces an inward pressure driving collapse and the latter a stabilizing outward pressure generated by random motion and energy dispersion. Since a contracting self-gravitating system is heated up one may wonder why is gravitational collapse not halted in all cases at a sufficient

We use the generalized uncertainty principle to compute the first correction to the Hawking temperature associated to Hawking effect. From this value we obtain a new evaporation time and entropy of any Schwarzschild black hole analyzing their expressions and consequences.

Quantum entanglement is regarded as one of the core concepts, which is used to describe the non-classical correlation between subsystems, and entropic uncertainty relation plays a vital role in quantum precision measurement. It is well known that entanglement of formation can be expressed by von Neumann entropy of subsystems for arbitrary pure states. An interesting question is naturally raised: is

In this work, we present a unified transformation method directly by using the inverse scattering method for a generalized derivative nonlinear Schrödinger (DNLS) equation. By establishing a matrix Riemann–Hilbert problem and reconstructing potential function q ( x , t ) from eigenfunctions ##IMG## [http://ej.iop.org/images/0253-6102/73/1/015002/ctpabc3acieqn1.gif] {${\{{G}_{j}(x,t,\eta )\}}_{1}^{3}$}

Considering the mass splittings of three active neutrinos, we investigate how the properties of dark energy affect the cosmological constraints on the total neutrino mass ##IMG## [http://ej.iop.org/images/0253-6102/72/12/125402/ctpabbb84ieqn1.gif] {$\sum {m}_{\nu }$} using the latest cosmological observations. In this paper, several typical dark energy models, including ΛCDM, w CDM, CPL, and HDE models

We investigate the quantum numbers of the pentaquark states ##IMG## [http://ej.iop.org/images/0253-6102/72/12/125202/ctpabb7cdieqn3.gif] {${{\rm{P}}}_{{\rm{c}}}^{+}$} , which are composed of 4 (three flavors) quarks and an antiquark, by analyzing their inherent nodal structure in this paper. Assuming that the four quarks form a tetrahedron or a square, and the antiquark is at the ground state, we determine

The (1 + 2)-dimensional chiral nonlinear Schrödinger equation (2D-CNLSE) as a nonlinear evolution equation is considered and studied in a detailed manner. To this end, a complex transform is firstly adopted to arrive at the real and imaginary parts of the model, and then, the modified Jacobi elliptic expansion method is formally utilized to derive soliton and other solutions of the 2D-CNLSE. The exact

In this letter, we investigate multisoliton solutions with even numbers and its generated solutions for nonlocal Fokas–Lenells equation over a nonzero background. First, we obtain 2 n -soliton solutions with a nonzero background via n -fold Darboux transformation, and find that these soliton solutions will appear in pairs. Particularly, 2 n -soliton solutions consist of n ‘bright’ solitons and n ‘dark’

Based on a special transformation that we introduce, the N -soliton solution of the (2+1)-dimensional Boiti–Leon–Manna–Pempinelli equation is constructed. By applying the long wave limit and restricting certain conjugation conditions to the related solitons, some novel localized wave solutions are obtained, which contain higher-order breathers and lumps as well as their interactions. In particular

The momentum distribution and dynamical structure factor in a weakly interacting Bose gas with a time-dependent periodic modulation in terms of the Bogoliubov treatment are investigated. The evolution equation related to the Bogoliubov weights happens to be a solvable Mathieu equation when the coupling strength is periodically modulated. An exact relation between the time derivatives of momentum distribution

The retrieval of lost entanglement for relatively accelerated fermionic observers of a tripartite system by a partial measurement technique has been investigated. From the prospective of the negativities of one-tangles and the π -tangle, we show that the degraded entanglement in noninertial frames with single-mode approximation is completely retrieved by an optimal strength of the partial measurement

This article concerns the analysis of an unsteady stagnation point flow of Eyring–Powell nanofluid over a stretching sheet. The influence of thermophoresis and Brownian motion is also considered in transport equations. The nonlinear ODE set is obtained from the governing nonlinear equations via suitable transformations. The numerical experiments are performed using the Galerkin scheme. A tabular form

We propose a modified version of the Faddeev–Popov (FP) quantization approach for non-Abelian gauge field theory to avoid Gribov ambiguity. We show that by means of introducing a new method of inserting the correct identity into the Yang–Mills generating functional and considering the identity generated by an integral through a subgroup of the gauge group, the problem of Gribov ambiguity can be removed

We investigate the quantum-memory-assisted entropic uncertainty relation (QMA-EUR) in a Heisenberg XYZ mixed-spin (1/2, 1) model. Coupling strength, Dzyaloshinskii–Moriya (DM) interaction and inhomogeneous magnetic field, respectively, contributing to QMA-EUR by a thermal entanglement in the hybrid-spin model are studied in detail. Furthermore, we compare the uncertainty of the bipartite hybrid model

We explore the non-commutative (NC) effects on the energy spectrum of a two-dimensional hydrogen atom. We consider a confined particle in a central potential and study the modified energy states of the hydrogen atom in both coordinates and momenta of non-commutativity spaces. By considering the Rashba interaction, we observe that the degeneracy of states can also be removed due to the spin of the particle

We propose a systematic method to construct the Mel’nikov model of long–short wave interactions, which is a special case of the Kadomtsev–Petviashvili (KP) equation with self-consistent sources (KPSCS). We show details how the Cauchy matrix approach applies to Mel’nikov's model which is derived as a complex reduction of the KPSCS. As a new result we find that in the dispersion relation of a 1-soliton

In this paper, we propose an innovative chaotic system, combining fractional derivative and sine-hyperbolic nonlinearity with circuit execution. The study of this system is conducted via an analog circuit simulator, using two anti-parallel semiconductor diodes to provide hyperbolic sine nonlinearity, and to function as operational amplifiers. The multi-stability of the system is also enhanced with

Dark solitons in the inhomogeneous optical fiber are studied in this manuscript via a higher-order nonlinear Schrödinger equation, since dark solitons can be applied in waveguide optics as dynamic switches and junctions or optical logic devices. Based on the Lax pair, the binary Darboux transformation is constructed under certain constraints, thus the multi-dark soliton solutions are presented. Soliton

In this paper, a new (3+1)-dimensional nonlinear evolution equation is introduced, through the generalized bilinear operators based on prime number p = 3. By Maple symbolic calculation, one-, two-lump, and breather-type periodic soliton solutions are obtained, where the condition of positiveness and analyticity of the lump solution are considered. The interaction solutions between the lump and multi-kink

In this work, we investigate the constraints on the total neutrino mass in the scenario of vacuum energy interacting with cold dark matter (abbreviated as IΛCDM) by using the latest cosmological observations. We consider four typical interaction forms, i.e. ##IMG## [http://ej.iop.org/images/0253-6102/72/12/125401/ctpabb7c9ieqn1.gif] {$Q=\beta H{\rho }_{\mathrm{de}}$} , ##IMG## [http://ej.iop.org/i

In this paper, the fractional-order model is used to study dust acoustic rogue waves in dusty plasma. Firstly, based on control equations, the multi-scale analysis and reduced perturbation method are used to derive the (3+1)-dimensional modified Kadomtsev–Petviashvili (MKP) equation. Secondly, using the semi-inverse method and the fractional variation principle, the (3+1)-dimensional time-fractional

We investigate the photon polarization tensor at finite temperatures in the presence of a static and homogeneous external magnetic field. In our scheme, the summing of the Matsubara frequency is performed after Poisson resummation, which is easily completed and converges quickly. Moreover, the behaviors of finite Landau levels are presented explicitly. It shows a convergence while summing infinite

In this work, the reaction ##IMG## [http://ej.iop.org/images/0253-6102/72/11/115303/ctpabb7daieqn5.gif] {${\pi }^{-}p\to {K}^{* }{{\rm{\Sigma }}}^{* }$} is investigated with an effective Lagrangian approach. The contributions from the Born terms, including the s , t , and u channel, are considered, and the Regge model and the Feynman model are applied to treat the t -channel contribution. The existing

Now, there have been many different methods to calculate one-loop amplitudes. Two of them are the unitarity cut method and the generalized unitarity cut method. In this short paper, we present an explicit connection between these two methods, especially how the extractions of triangle and bubble coefficients are equivalent to each other.

In our previous work (Meng et al 2020 Phys. Rev. A 101 023838), we discover the phenomenon that the quantum entanglement on the driving threshold line remains a constant in a three-mode optomechanical phonon laser system. In this paper, to find the conditions under which the constant boundary entanglement shows up, we explicitly study how this boundary entanglement depends on various parameters through

In this article we propose a four-level rubidium (Rb 87 ) atomic system for observing interesting features of polarization state rotation in a fast light medium. We investigate spontaneously generated coherence (SGC) for a spinning medium. We show how SGC can affect different spectral profiles of the polarization state and images in this suggested model. We observe a 0.5 radian rotation and 2.5 microsecond

A classical particle system coupled with a thermostat driven by an external constant force reaches its steady state when the ensemble-averaged drift velocity does not vary with time. In this work, the statistical mechanics of such a system is derived solely based on the equiprobability and ergodicity principles, free from any conclusions drawn on equilibrium statistical mechanics or local equilibrium

Charge-dependent correlations from both background and charge separation contribute to experimental observables in heavy-ion collisions. In this paper, we use stochastic hydrodynamics to study background charge asymmetry due to fluctuations. Using the rapidity-dependent correlation and a simple ansatz for particle distributions, we find a fluctuation-induced correlation to provide a type of background

In practical quantum key distribution (QKD) systems, a single photon-detector (SPD) is one of the most vulnerable components. Faint after-gate attack is a universal attack against the detector. However, the original faint after-gate attack can be discovered by monitoring the photocurrent. This paper presents a probabilistic generalization of the attack, which we refer to as probabilistic faint after-gate

Under investigation in this paper is a generalized (3+1)-dimensional Kadomtsev–Petviashvili equation in fluid dynamics and plasma physics. Soliton and one-periodic-wave solutions are obtained via the Hirota bilinear method and Hirota–Riemann method. Magnitude and velocity of the one soliton are derived. Graphs are presented to discuss the solitons and one-periodic waves: the coefficients in the equation

It has still been difficult to solve nonlinear evolution equations analytically. In this paper, we present a deep learning method for recovering the intrinsic nonlinear dynamics from spatiotemporal data directly. Specifically, the model uses a deep neural network constrained with given governing equations to try to learn all optimal parameters. In particular, numerical experiments on several third-order

In this paper, we study the influences of magnetic fields on the coexistence of diquark and chiral condensates in an extended Nambu–Jona–Lasinio model with QCD axial anomaly, as it relates to color-flavor-locked quark matter. Due to the coupling of rotated-charged quarks to magnetic fields, diquark condensates become split, and the coexistence region is thus superseded in favor of a specific diquark

By a combination method of Lee–Low–Pines unitary transformation method and Pekar-type variational method, the ground state energy (GSE) of the bound polaron is studied in the asymmetrical Gaussian potential quantum well considering the temperature and electromagnetic field. The impacts of the temperature and asymmetrical Gaussian potential, electromagnetic field and phonon–electron coupling upon the

The mechanical anisotropy, structural properties, electronic band structures and thermal properties of C 2 N 2 (CH 2 ), Si 2 N 2 (SiH 2 ) and Ge 2 N 2 (GeH 2 ) are detailed and investigated in this work. The novel silicon nitride phase Si 2 N 2 (SiH 2 ) and germanium nitride phase Ge 2 N 2 (GeH 2 ) in the Cmc 2 1 structure are proposed in this work. The novel proposed Si 2 N 2 (SiH 2 ) and Ge 2 N 2

Superperiodicity, chaos and coexisting orbits of ion-acoustic waves (IAWs) are studied in a multi-component plasma consisting of fluid ions, q -nonextensive cold and hot electrons and Maxwellian hot positrons. The significant impacts of the system parameters on superperiodic and nonlinear periodic IAWs are presented. Considering an external periodic perturbation various types of quasiperiodic and chaotic

Investigating the dynamic characteristics of nonlinear models that appear in ocean science plays an important role in our lifetime. In this research, we study some features of the paired Boussinesq equation that appears for two-layered fluid flow in the shallow water waves. We extend the modified expansion function method (MEFM) to obtain abundant solutions, as well as to find new solutions. By using

To describe two correlated events, the Alice–Bob (AB) systems were constructed by Lou through the symmetry of the shifted parity, time reversal and charge conjugation. In this paper, the coupled AB system of the Kadomtsev–Petviashvili equation, which is a useful model in natural science, is established. By introducing an extended Bäcklund transformation and its bilinear formation, the symmetry breaking

We revisit the novel symmetries in ##IMG## [http://ej.iop.org/images/0253-6102/72/10/105205/ctpaba24fieqn3.gif] {${ \mathcal N }=2$} supersymmetric quantum mechanical models by considering specific examples of coupled systems. Further, we extend our analysis to a general case and list out all the novel symmetries. In each case, we show the existence of two sets of discrete symmetries that correspond

Solving nonlinear evolution partial differential equations has been a longstanding computational challenge. In this paper, we present a universal paradigm of learning the system and extracting patterns from data generated from experiments. Specifically, this framework approximates the latent solution with a deep neural network, which is trained with the constraint of underlying physical laws usually

Car taillights are ubiquitous during the deceleration process in real traffic, while drivers have a memory for historical information. The collective effect may greatly affect driving behavior and traffic flow performance. In this paper, we propose a continuum model with the driver’s memory time and the preceding vehicle’s taillight. To better reflect reality, the continuous driving process is also

The economic and financial systems consist of many nonlinear factors that make them behave as the complex systems. Recently many chaotic finance systems have been proposed to study the complex dynamics of finance as a noticeable problem in economics. In fact, the intricate structure between financial institutions can be obtained by using a network of financial systems. Therefore, in this paper, we