Introducing ${ \mathcal P }{ \mathcal T }$-symmetric generalized Scarf-II potentials into the three-coupled nonlinear Gross–Pitaevskii equations offers a new way to seek stable soliton states in quasi-one-dimensional spin-1 Bose–Einstein condensates. In scenarios where the spin-independent parameter c0 and the spin-dependent parameter c2 vary, we use both analytical and numerical methods to investigate the three-coupled nonlinear Gross–Pitaevskii equations with ${ \mathcal P }{ \mathcal T }$-symmetric generalized Scarf-II potentials. We obtain analytical soliton states and find that simply modulating c2 may change the analytical soliton states from unstable to stable. Additionally, we obtain numerically stable double-hump soliton states propagating in the form of periodic oscillations, exhibiting distinct behavior in energy exchange. For further investigation, we discuss the interaction of numerical double-hump solitons with Gaussian solitons and observe the transfer of energy among the three components. These findings may contribute to a deeper understanding of solitons in Bose–Einstein condensates with ${ \mathcal P }{ \mathcal T }$-symmetric potentials and may hold significance for both theoretical understanding and experimental design in related physics experiments.
We study fundamental dark-bright solitons and the interaction of vector nonlinear Schrödinger equations in both focusing and defocusing regimes. Classification of possible types of soliton solutions is given. There are two types of solitons in the defocusing case and four types of solitons in the focusing case. The number of possible variations of two-soliton solutions depends on this classification. We demonstrate that only special types of two-soliton solutions in the focusing regime can generate breathers of the scalar nonlinear Schrödinger equation. The cases of solitons with equal and unequal velocities in the superposition are considered. Numerical simulations confirm the validity of our exact solutions.
To solve the Poisson equation it is usually possible to discretize it into solving the corresponding linear system Ax = b. Variational quantum algorithms (VQAs) for the discretized Poisson equation have been studied before. We present a VQA based on the banded Toeplitz systems for solving the Poisson equation with respect to the structural features of matrix A. In detail, we decompose the matrices A and A2 into a linear combination of the corresponding banded Toeplitz matrix and sparse matrices with only a few non-zero elements. For the one-dimensional Poisson equation with different boundary conditions and the d-dimensional Poisson equation with Dirichlet boundary conditions, the number of decomposition terms is less than that reported in [Phys. Rev. A 2023 108, 032 418 ]. Based on the decomposition of the matrix, we design quantum circuits that efficiently evaluate the cost function. Additionally, numerical simulation verifies the feasibility of the proposed algorithm. Finally, the VQAs for linear systems of equations and matrix-vector multiplications with the K-banded Toeplitz matrix TnK are given, where ${T}_{n}^{K}\in {R}^{n\times n}$ and $K\in O(\mathrm{ploylog}n)$ .
In this paper, we propose a new non-Gaussian quantum state, termed the photon-modulated displaced thermal state (DTS). Using the operator ordering method, we obtain the normal ordering product of its density operator and then investigate its normalization, the negativity of its Wigner function and its non-Gaussianity.
The decoherence of high-dimensional orbital angular momentum (OAM) entanglement in the weak scintillation regime has been investigated. In this study, we simulate atmospheric turbulence by utilizing a multiple-phase screen imprinted with anisotropic non-Kolmogorov turbulence. The entanglement negativity and fidelity are introduced to quantify the entanglement of a high-dimensional OAM state. The numerical evaluation results indicate that entanglement negativity and fidelity last longer for a high-dimensional OAM state when the azimuthal mode has a lower value. Additionally, the evolution of higher-dimensional OAM entanglement is significantly influenced by OAM beam parameters and turbulence parameters. Compared to isotropic atmospheric turbulence, anisotropic turbulence has a lesser influence on high-dimensional OAM entanglement.
Improvement of the detection ability of quantum entanglement is one of the essential tasks in quantum computing and quantum information. Finite tight frames play a fundamental role in a wide variety of areas and, generally, each application requires a specific class of frames and is closely related to quantum measurement. It is worth noting that a maximal set of complex equiangular vectors is closely related to a symmetric informationally complete measurement. Hence, our goal in this work is to propose a series of separability criteria assigned to a finite tight frame and some well-known inequalities in different quantum systems, respectively. In addition, some tighter criteria to detect entanglement for many-body quantum states are presented in arbitrary dimensions. Finally, the effectiveness of the proposed entanglement detection criteria is illustrated through some detailed examples.
In science and technology, precision measurement of physical quantities is crucial, and the quantum Fisher information (QFI) plays a significant role in the study of quantum systems. In this work, we explore the dynamics of QFI in a hybrid optomechanical system, which consists of a ♢-type four-level atom interacting with a single-mode quantized field via a multi-photon process. We account for various sources of dissipation, including the decay rates of the atom, the cavity and the mechanical modes. Using an effective Hamiltonian, we analytically derive the explicit form of the state vector of the entire system via the time-dependent Schrödinger equation. We then investigate the atomic QFI for the estimation precision of the decay rate of the mechanical oscillator. Furthermore, we examine how optomechanical and atom-field coupling strengths, dissipation parameters and multi-photon transition influence the dynamics of atomic QFI. Our numerical results suggest that the estimation precision of the decay rate of the mechanical oscillator can be controlled by these parameters.
The magnetic behavior of a two-electron quantum dot/ring system is analytically studied with electron–electron (e–e) interaction taking into account the Rashba spin–orbit interaction (SOI) and magnetic field. The Jacobi transformation has been employed to separate the Hamiltonian of the system to the center of mass and relative terms. The Schrödinger equation is analytically solved, and energy spectra are obtained. Then, the magnetization and susceptibility are calculated. The magnetization decreases by raising the magnetic field without and with SOI, and also without e-e interaction. Also, the SOI slightly modifies the magnetization of the system without e–e interaction. The susceptibility displays a peak structure as the magnetic field changes from low values to high values. The susceptibility by considering e–e interaction and without the SOI is always negative and its value decreases by rising the magnetic field. The susceptibility displays a transition from diamagnetic to paramagnetic with e–e interaction and SOI.
In this work, we investigate the thermodynamic variables of a harmonic oscillator in a conical geometry metric. Moreover, we introduce an external field in the form of a Wu–Yang magnetic monopole (WYMM) and an inverse square potential into the system and analyze the results. Using an analytical approach, we obtain the energy level and study the thermodynamics at finite temperature. Our findings demonstrate that thermodynamic variables, except for the specific heat and entropy, are influenced by the topological parameters, the strength of the WYMM, and the inverse square potential.
The presence of background classical sources affects quantum field theory significantly in different ways. Neutrino oscillation is a phenomenon that confirms that neutrinos are massive fermions in nature, a celebrated result in modern physics. Neutrino oscillation plays an important role in many astrophysical observations. However, the interactions between the background classical sources with neutrinos are not often considered. In the present article, we show the effect of some classical sources, namely matter currents, electromagnetic waves, torsion, and gravitational waves on neutrino oscillation. It is shown explicitly that the above sources can change the helicity state of neutrinos during neutrino oscillation.
We simulate the gravitational redshift of quantum matter waves with a long de Broglie wavelength by tracing particle beams along geodesics, when they propagate within the rotation plane of binary black holes. The angular momentum of the binary black hole causes an asymmetric gravitational redshift distribution around the two black holes. The gravitational redshift changes the frequency of quantum matter waves and their wavelength, resulting in the different interference patterns of quantum matter waves with respect to different wavelengths. The interference pattern demonstrates strong contrast intensity and spatial order with respect to different wavelengths and the rotational angle of the binary black hole. A bright semicircular arc emerges from the interference pattern to bridge the two black holes, when they rotate to certain angles, which provides a theoretical understanding on the gravitational lensing effect of quantum matter waves.
This paper aims to develop non-interacting ghost dark energy and generalized ghost dark energy models within the framework of f(Q) theory using the correspondence scheme. We use pressureless matter and a power-law scale factor. The cosmic implications of the resulting models are studied through the equation of state parameter and the phase planes. We also check the stability of the reconstructed models through the squared speed of sound parameter. The equation of state parameter exhibits a phantom era, the $({\omega }_{D}-{\omega }_{D}^{{\prime} })$ -plane indicates a freezing region, while the (r−s)-plane corresponds to the Chaplygin gas model for both models. It is also found that only the generalized ghost dark energy model remains stable throughout cosmic evolution. We conclude that our findings align well with current observational data.
We have examined an isotropic and homogeneous cosmological model in f(R, Tφ) gravity, where R represents the Ricci scalar and Tφ exhibits the energy momentum tensor’s trace. We examine the stability criteria by performing the dynamical system analysis for our model f(R, Tφ) = R + 2(aTφ + b), where a and b are the constants. We derive a set of autonomous equations and find their solutions by assuming a flat potential V0. We assess the equilibrium points from these equations and find the eigenvalues. We analyze the physical interpretation of the phase space for this system. We obtain three stable equilibrium points. We also examine the interaction between the scalar field and dark energy, represented by Q = $\Psi$Hρde and determine the equilibrium points for this interaction. We identify four stable equilibrium points for this interaction. We calculate the values of the physical parameters for both scenarios at each equilibrium point, indicating the Universe’s accelerated expansion.
We assume exponential corrections to the entropy of 5D charged AdS black hole solutions, which are derived within the framework of Einstein–Gauss–Bonnet gravity and nonlinear electrodynamics. Additionally, we consider two distinct versions of 5D charged AdS black holes by setting the parameters q → 0 and k → 0 (where q represents the charge, and k is the non-linear parameter). We investigate these black holes in the extended phase space, where the cosmological constant is interpreted as pressure, demonstrating the first law of black hole thermodynamics. The focus extends to understanding the thermal stability or instability, as well as identifying first and second-order phase transitions. This exploration is carried out through the analysis of various thermodynamic quantities, including heat capacity at constant pressure, Gibbs free energy (GFE), Helmholtz free energy (HFE), and the trace of the Hessian matrix. In order to visualize phase transitions, identify critical points, analyze stability and provide comprehensive analysis, we have made the contour plot of the mentioned thermodynamic quantities and observed that our results are very consistent. These investigations are conducted within the context of exponentially corrected entropies, providing valuable insights into the intricate thermodynamic behavior of these 5D charged AdS black holes under different parameter limits.
The tunneling conductance of two kinds of tunnel junctions with time-reversal symmetry breaking, normal metal/insulator/ferromagnetic metal/ ${d}_{{x}^{2}-{y}^{2}}+i{s}$ -wave superconductor (NM/I/FM/ ${d}_{{x}^{2}-{y}^{2}}+i{s}$ -wave SC) and NM/I/FM/ ${d}_{{x}^{2}-{y}^{2}}+i{{d}}_{xy}$ -wave SC, is calculated using the extended Blonder–Tinkham–Klapwijk theoretical method. The ratio of the subdominant s-wave and ${d}_{xy}$ -wave components to the dominant ${d}_{{x}^{2}-{y}^{2}}$ -wave component is expressed by $\displaystyle \frac{{{\rm{\Delta }}}_{s}}{{{\rm{\Delta }}}_{D}}$ and $\displaystyle \frac{{{\rm{\Delta }}}_{d}}{{{\rm{\Delta }}}_{D}},$ respectively. Results show that for NM/I/FM/ ${d}_{{x}^{2}-{y}^{2}}+is$ -wave SC tunnel junctions, the splitting of the zero-bias conductance peak (ZBCP) is obtained and the splitting peaks appear at $\displaystyle \frac{eV}{{{\rm{\Delta }}}_{0}}=\pm \displaystyle \frac{{{\rm{\Delta }}}_{s}}{{{\rm{\Delta }}}_{D}}$ with eV the applied bias voltage and ${{\rm{\Delta }}}_{0}$ the zero temperature energy gap of SC. For NM/I/FM/ ${d}_{{x}^{2}-{y}^{2}}+i{d}_{xy}$ -wave SC tunnel junctions, there are also conductance peaks at $\displaystyle \frac{eV}{{{\rm{\Delta }}}_{0}}=\pm \displaystyle \frac{{{\rm{\Delta }}}_{d}}{{{\rm{\Delta }}}_{D}},$ but the ZBCP does not split. For the two types of tunnel junctions, the completely reversed tunnel conductance spectrum indicates that when the exchange energy in FM is increased to a certain value, the proximity effect transforms the tunnel junctions from the ‘0 state’ to the ‘π state’. The shortening of the transport quasiparticle lifetime can weaken the proximity effect to smooth out the dips and peaks in the tunnel spectrum. This is considered a possible reason that the ZBCP splitting was not observed in some previous experiments. It is expected that these analysis results can serve as a guide for future experiments and the relevant conclusions can be confirmed.
We aim to find one highly nontrivial example of the solutions to the vortex fluid dynamical equation on the unit sphere (S2) and compare it with the numerical simulation. Since the rigid rotating steady solution for vortex fluids on S2 is already known to us, we consider the perturbations above it. After decomposing the perturbation of the vortex number density and vortex charge density into spherical harmonics, we find that the perturbations are propagating waves. To be precise, the velocities for different single-mode vortex number density waves are all the same, while the velocities for single-mode vortex charge density waves depend on the degree of the spherical harmonics l, which is a signal of the existence of dispersion. Meanwhile, we find that there is a beat phenomenon for the positive (or negative) vortex density wave. Numerical simulation based on the canonical equations for the point vortex model agrees perfectly with our theoretical calculations.
Utilizing the dissipative Gross–Pitaevskii equation, we investigated the splitting dynamics of triply quantized vortices at finite temperature. Through linear perturbation analysis, we determined the excitation modes of these vortices across various dissipation parameters. We identified three unstable modes with p = 2-, 3- and 4-fold rotational symmetries, revealing a significant dynamic transition of the most unstable mode. That is, as the dissipation parameter increases the most unstable mode transitions from the p = 2 mode to the p = 3 mode. Throughout the entire range of dissipation parameters, the p = 4 unstable mode is never the dominant mode. Subsequently, we performed nonlinear numerical simulations of the vortex splitting process. Under random perturbations we confirmed the dynamical transition, and under specific perturbations we confirmed the instability of the p = 4 mode. Our findings on the finite temperature dependence of the splitting dynamics of triply quantized vortices are expected to be verifiable in experiments.
