In this paper, the Drinfeld–Sokolov–Satsuma–Hirota (DSSH) system is studied by using residual symmetry and the consistent Riccati expansion (CRE) method, respectively. The residual symmetry of the DSSH system is localized to Lie point symmetry in a properly prolonged system, based on which we get a new Bäcklund transformation for this system. New symmetry reduction solutions of the DSSH system are obtained by applying the classical Lie group approach on the prolonged system. Moreover, the DSSH system proves to be CRE integrable and new interesting interaction solutions between solitons and periodic waves are generated and analyzed.

The damped Helmholtz–Duffing oscillator is a topic of great interest in many different fields of study due to its complex dynamics. By transitioning from conventional continuous differential equations to their fractal counterparts, one gains insights into the system's response under new mathematical frameworks. This paper presents a novel method for converting standard continuous differential equations into their fractal equivalents. This conversion occurs after the nonlinear system is transformed into its linear equivalent. Numerical analyses show that there are several resonance sites in the fractal system, which differ from the one resonance point found in the continuous system. One important finding is that the fractal system loses some of its stabilizing power when decaying behavior is transformed into a diffuse pattern. Interestingly, a decrease in the fractal order in resonance settings shows a stabilizing impact, highlighting the dynamics' complexity inside fractal systems. This endeavor to convert to fractals is a revolutionary technique that is being employed for the first time.

In this paper, a variable-coefficient modified Kadomtsev–Petviashvili (vcmKP) system is investigated by modeling the propagation of electromagnetic waves in an isotropic charge-free infinite ferromagnetic thin film and nonlinear waves in plasma physics and electrodynamics. Painlevé analysis is given out, and an auto-Bäcklund transformation is constructed via the truncated Painlevé expansion. Based on the auto-Bäcklund transformation, analytic solutions are given, including the solitonic, periodic and rational solutions. Using the Lie symmetry approach, infinitesimal generators and symmetry groups are presented. With the Lagrangian, the vcmKP equation is shown to be nonlinearly self-adjoint. Moreover, conservation laws for the vcmKP equation are derived by means of a general conservation theorem. Besides, the physical characteristics of the influences of the coefficient parameters on the solutions are discussed graphically. Those solutions have comprehensive implications for the propagation of solitary waves in nonuniform backgrounds.

We use out-of-time order correlators (OTOCs) to investigate the quantum instability and Ehrenfest time for an inverted harmonic oscillator (IHO). For initial states located in the stable manifolds of the IHO we find that the corresponding OTOC exhibits identical evolutionary characteristics to the saddle point before the Ehrenfest time. For initial states located in the unstable manifolds, the OTOCs still grow exponentially but the time to maintain exponential growth is related to the center position of its wave packet in phase space. Moreover, we use the Husimi Q function to visualize the quantum wave packets during exponential growth of the OTOCs. Our results show that quantum instability exists at arbitrary orbits in the IHO system, and the Ehrenfest time in the IHO system depends not only on the photon number of the initial system but also on the central positions of the initial states in phase space.

We connect magic (non-stabilizer) states, symmetric informationally complete positive operator valued measures (SIC-POVMs), and mutually unbiased bases (MUBs) in the context of group frames, and study their interplay. Magic states are quantum resources in the stabilizer formalism of quantum computation. SIC-POVMs and MUBs are fundamental structures in quantum information theory with many applications in quantum foundations, quantum state tomography, and quantum cryptography, etc. In this work, we study group frames constructed from some prominent magic states, and further investigate their applications. Our method exploits the orbit of discrete Heisenberg–Weyl group acting on an initial fiducial state. We quantify the distance of the group frames from SIC-POVMs and MUBs, respectively. As a simple corollary, we reproduce a complete family of MUBs of any prime dimensional system by introducing the concept of MUB fiducial states, analogous to the well-known SIC-POVM fiducial states. We present an intuitive and direct construction of MUB fiducial states via quantum T-gates, and demonstrate that for the qubit system, there are twelve MUB fiducial states, which coincide with the H-type magic states. We compare MUB fiducial states and SIC-POVM fiducial states from the perspective of magic resource for stabilizer quantum computation. We further pose the challenging issue of identifying all MUB fiducial states in general dimensions.

The fractional shortcut to adiabaticity (f-STA) for the production of quantum superposition states is proposed firstly via a three-level system with a Λ-type linkage pattern and a four-level system with a tripod structure. The fast and robust production of the coherent superposition states is studied by comparing the populations for the f-STA and the fractional stimulated Raman adiabatic passage (f-STIRAP). The states with equal proportions can be produced by fixing the controllable parameters of the driving pulses at the final moment of the whole process. The effects of the pulse intensity and the time delay of the pulses on the production process are discussed by monitoring the populations on all of the quantum states. In particular, the spontaneous emission arising from the intermediate state is investigated by the quantum master equation. The result reveals that the f-STA exhibits superior advantages over the f-STIRAP in producing the superposition states.

In this paper, we develop a quantum communication protocol for the simultaneous preparation of a two-qubit and a three-qubit state at the positions of two different parties situated spatially apart. For one party, Alice, it is a remote state preparation of a known two-qubit state while for the other party, Bob, it is a joint remote state preparation with the help of a third party, Eve. The protocol is executed in a hybrid form bi-directionally in the presence of two controllers, Charlie and David. There is a hierarchy in the process through different levels of control under which the actions by Alice and Bob are performed. There is a need for a ten-qubit entangled channel connecting the five parties. The generation of this channel through a circuit is discussed. The protocol is executed on the IBM Quantum platform. We also study the effect of noise on our protocol. Here, amplitude-damping, bit-flip and phase-flip noisy environments are considered and the corresponding variations of fidelity are theoretically and numerically analyzed.

We use the Schrödinger–Newton equation to calculate the regularized self-energy of a particle using a regular self-gravitational and electrostatic potential derived in string T-duality. The particle mass M is no longer concentrated into a point but is diluted and described by a quantum-corrected smeared energy density resulting in corrections to the energy of the particle, which is interpreted as a regularized self-energy. We extend our results and find corrections to the relativistic particles using the Klein–Gordon, Proca and Dirac equations. An important finding is that we extract a form of the generalized uncertainty principle (GUP) from the corrected energy. This form of the GUP is shown to depend on the nature of particles; namely, for bosons (spin 0 and spin 1) we obtain a quadratic form of the GUP, while for fermions (spin 1/2) we obtain a linear form. The correlation we find between spin and GUP may offer insights for investigating quantum gravity.

We revisit the issue of whether the effective potential for the conformal factor of the metric, which is generated by quantized matter fields, possesses a non-vanishing vacuum expectation value (VEV) or not. We prove that the effective potential has a vanishing vacuum expectation value on the basis of a global GL(4) symmetry. We also account for why there seems to be two different effective potentials for the conformal factor in a theory, one of which gives rise to a vanishing VEV for the conformal factor, whereas the other has a non-vanishing VEV.

In this study, we investigated worldvolume fermions on the flavor brane in the D0–D4/D8 model, which is holographically equivalent to four-dimensional quantum chromodynamics with instantons or equivalently with a theta angle. The action involving the worldvolume fermions was obtained by the T-duality rules in string theory, and we accordingly derived their effective five-dimensional and canonical four-dimensional forms by using the systematic dimensional reduction and decomposition of the spinor. Subsequently, we used the AdS/CFT dictionary to evaluate the two-point correlation function as the spectral function for the worldvolume fermions and interpreted the fermions as baryons by analyzing their quantum number with the baryon vertex in holography. In this sense, the interacted action involving the worldvolume fermions and gauge field on the flavor brane was finally derived in holography, which describes the various interactions of mesons and baryons with instantons in the large-N limit. Therefore, this study provides a holographic picture to describe baryons and their interactions based on string theory, particularly in the presence of instantons or a theta angle.

Research on the properties of neutron stars with dark energy is a particularly interesting yet unresolved problem in astrophysics. We analyze the influence of dark energy on the equation of state, the maximum mass, the surface gravitational redshift and the Keplerian frequency for the traditional neutron star and the hyperon star matter within the relativistic mean field theory, using the GM1 and TM1 parameter sets by considering the two flavor symmetries of SU(6) and SU(3) combined with the observations of PSR J1614-2230, PSR J0348+0432, PSR J0030+0451, RX J0720.4-3125, and 1E 1207.4-5209. It is found that the existence of dark energy leads to the softened equations of the state of the traditional neutron star and the hyperon star. The radius of a fixed-mass traditional neutron star (or hyperon star) with dark energy becomes smaller, which leads to increased compactness. The existence of dark energy can also enhance the surface gravitational redshift and the Keplerian frequency of traditional neutron stars and hyperon stars. The growth of the Keplerian frequency may cause the spin rate to speed up, which may provide a possible way to understand and explain the pulsar glitch phenomenon. Specifically, we infer that the mass and the surface gravitational redshift of PSR J1748-2446ad without dark energy for the GM1 (TM1) parameter set are 1.141 M_⊙ (1.309 M_⊙) and 0.095 (0.105), respectively. The corresponding values for the GM1 (TM1) parameter set are 0.901 M_⊙ (1.072M_⊙) and 0.079 (0.091) if PSR J1748-2446ad contains dark energy with α = 0.05. PSR J1748-2446ad may be a low-mass pulsar with a lower surface gravitational redshift under our selected models.

In this paper, we investigate the optical properties of a non-rotating charged black hole (BH) in the Einstein–Maxwell-scalar (EMS) theory, together with a plasma medium. We first consider the photon sphere and shadow radius under the impact of the plasma medium existing in the environment surrounding the BH in the EMS theory. We show that the radius of the photon sphere and the BH shadow decrease under the influence of the parameter β. We further study gravitational weak lensing in detail by adapting general methods and derive the light ray's deflection angle around the BH together with the plasma environment. It is found that for uniform plasma, the deflection angle increases with the rise of the plasma parameter, whereas it decreases with the increase of the plasma parameter for non-uniform plasma. Besides, we also study the magnification of image brightness.

In the present article, we introduce a completely new regular model for static, spherically symmetric celestial fluid spheres in embedding class I spacetime. In this regard, needfully, we propose a new suitable metric potential e^λ(r) to generate the present model. The various analyses on energy density, pressure, anisotropic factor, mass, compactness parameter, redshift, and energy condition make sure the model is physically viable on the ground of model stars Vela X-1, Cen X-3, SMC X-4, and LMC X-4. The reported solutions also respect the equilibrium state by satisfying the Tolman–Oppenheimer–Volkoff (TOV) equation and ensure stability by satisfying the causality condition, condition on the adiabatic index, and Harrison–Zeldovich–Novikov condition. The generated M − R graph matches the ranges of masses and radii for the model compact stars. Additionally, this study provides estimates of the moment of inertia based on the I − M graph.

Gas targets have been used to measure the scattering length in neutron–proton (n–p) scattering experiments. Changes in electron dynamics within the gas target have a negligible effect on the dynamics of nucleons. However, electron dynamics are sensitively related to the specific form of the n–p interaction during the scattering process. We propose a theoretical approach to explore electron dynamics and determine the parameters of the n–p interaction. This approach is based on a three-body scattering process involving a neutron, a proton and an electron. Numerical results indicate significant differences in electron dynamics with varying values of n–p interaction parameters, providing additional information beyond scattering cross-sections to accurately determine these parameters.

A way to enhance the growth of stimulated Raman instability in laser-plasma interactions was investigated. This relies on the application of density modulation of a co-propagating electron beam in plasmas. In the stimulated Raman scattering process, an electromagnetic pump wave decays into a low-frequency wave and a scattered electromagnetic sideband wave. In this process, the pump wave produces an oscillatory velocity associated with the plasma electrons and the beam electrons. These oscillatory velocities combine with the existing low-frequency mode, producing ponderomotive force that drives high-frequency sideband waves. The sidebands couple to the pump wave, driving the beam-mode. A modulation of the electron beam density enhances the growth rate of the instability. The theoretical calculations show about 40% enhancements in growth of Raman instability at resonance (where the electron beam density modulation parameter approaches to unity) for the plasma density of the order of 10¹⁸ cm⁻³.

We consider matter–wave solitons in spin–orbit coupled Bose–Einstein condensates embedded in an optical lattice and study the dynamics of the soliton within the framework of Gross–Pitaevskii equations. We express spin components of the soliton pair in terms of nonlinear Bloch equations and investigate the effective spin dynamics. It is seen that the effective magnetic field that appears in the Bloch equation is affected by optical lattices, and thus the optical lattice influences the precessional frequency of the spin components. We make use of numerical approaches to investigate the dynamical behavior of density profiles and center-of-mass of the soliton pair in the presence of the optical lattice. It is shown that the spin density is periodically varying due to flipping of spinors between the two states. The amplitude of spin-flipping oscillation increases with lattice strength. We find that the system can also exhibit interesting nonlinear behavior for chosen values of parameters. We present a fixed point analysis to study the effects of optical lattices on the nonlinear dynamics of the spin components. It is seen that the optical lattice can act as a control parameter to change the dynamical behavior of the spin components from periodic to chaotic.

In the multilayer film-substrate system, thermal stress concentration and stress mutations cause film buckling, delamination and cracking, leading to device failure. In this paper, we investigated a multilayer film system composed of a substrate and three film layers. The thermal stress distribution inside the structure was calculated by the finite element method, revealing significant thermal stress differences between the layers. This is mainly due to the mismatch of the coefficient of thermal expansion between materials. Different materials respond differently to changes in external temperature, leading to compression between layers. There are obvious thermal stress concentration points at the corners of the base layer and the transition layer, which is due to the sudden change of the shape at the geometric section of the structure, resulting in a sudden increase in local stress. To address this issue, we chamfered the substrate and added an intermediate layer between the substrate and the transition layer to assess whether these modifications could reduce or eliminate the thermal stress concentration points and extend the service life of the multilayer structure. The results indicate that chamfering and adding the intermediate layer effectively reduce stress discontinuities and mitigate thermal stress concentration points, thereby improving interlayer bonding strength.