International Journal of Theoretical Physics最新文献

In this paper, we investigate the integrability problem of the (2+1)-dimensional bidirectional Sawada-Kotera (bSK) equation. Through analyzing the model, we explore the characteristics of nonlinear dynamics. The Bell polynomial method is one of the most useful tools for studying the integrability of nonlinear evolution equations. Using this method, we derive the Bäcklund transformation, Lax pair, infinite many conservation laws, and nonlinear superposition formula of solutions for the (2+1)-dimensional bSK equation. Then, we constructed the lump-type solutions and soliton solutions of the equation respectively by utilizing its bilinear form and the nonlinear superposition formula of solutions. The dynamic behaviors of the lump-type solutions, lump-kink solutions, and interaction solutions of the model were deduced via the mathematical symbolic computation system Mathematica, the extended three-wave method, and the homo-clinic test method, with the relationship between local waves in physics being elaborated.

Nonlocality is a crucial concept for distinguishing between quantum theory and local hidden variable models, and it plays a significant role in building quantum computations. Therefore, this paper aims to explore the dynamics of generating different two-qubit nonlocalities in a single electron double quantum dot (EDQD) with spin-orbit interactions, including Rashba spin-orbit interaction and the Dzyaloshinsky–Moriya interaction. The nonlocality dynamics of the two EDQD qubits, induced by the intrinsic decoherence model, are explored through the violation of Bell inequalities, uncertainty-induced nonlocality, and entanglement of formation. For small couplings, the generated nonlocalities exhibit growth with irregular oscillatory dynamics. The regularity, magnitude, and frequency of these oscillatory dynamics are enhanced by increasing the coupling of Rashba and Dzyaloshinsky–Moriya spin-orbit interactions. Increasing the tunneling coupling reduces the ability of the EDQD-qubit system to generate Bell nonlocality and entanglement of formation. In contrast, it enhances uncertainty-induced nonlocality. The generation of two-EDQD-qubits nonlocality is examined under increasing couplings and intrinsic decoherence. It is found that the degradation in both the frequency and amplitude of the oscillatory dynamics associated with the generated nonlocalities is strongly dependent on the specific EDQD coupling parameters.

This article investigates the space fractional diffusion equation (SFDE). In this work, two efficient and precise numerical methods (Novel Shifted Jacobi Operational Matrix techniques) are applied for solving a category of these equations, converting the original problem into a set of algebraic equations that can be solved using numerical methods. The key benefit of these schemes is their ability to transform linear and nonlinear (PDE)s into a set of algebraic equations concerning the expansion coefficients of the solution. The suggested techniques are effectively utilized for the aforementioned problem. Sufficient and thorough numerical evaluations are provided to illustrate the precision, applicability, effectiveness, and adaptability of the techniques introduced. To demonstrate the effectiveness and accuracy of these techniques, the numerical results from the examples are presented in a table format to enable comparison with results from other established methods as well as with the precise solutions. It should be noted that the implementation of the current methods are considered very easy and general for many numerical techniques.

Despite the successful experimental generation and verification of genuine multipartite entanglement, several existing entanglement measures remain insufficient to reliably capture its presence. In this study, we overcome this challenge by utilizing a geometric measure known as concurrence fill, which quantifies genuine multipartite entanglement of pure states using the area associated with the underlying concurrence triangle. Firstly, the concurrence fill for three-qubit pure states is reformulated using three tangle and partial tangles. This yields a representation that is more tractable and operational. Using this formulation, we derive a criterion to classify GHZ and W class of states. Next, we analyse the rank-2 mixture of generalized GHZ and W class of states for which three-tangle is known to vanish over a zero polytope. Furthermore, we derive the concurrence fill for the eigenstates of the corresponding mixture and obtain its upper bound for mixed states with zero tangle.

In this paper, the variable coefficients Broer-Kaup-Kupershmit (vcBKK) equations undergo analysis through the Lie symmetry method, leading to the determination of their infinitesimal generators. The optimal system of vcBKK equations are constructed with the help of Olver’s method. Based on the optimal system, a multiple set of (1+1)-dimensional reduced equations are obtained by performing a symmetric reduction on the (2+1)-dimensional vcBKK equations. Using (left( {G'/G} right)) method, ((1/G')) method and ((G'/{G^2})) method respectively to solve the reduced equations. Several novel exact solutions for the vcBKK equations are derived. The impact of the coefficient functions on the solutions are explored by choosing various forms for the coefficient functions. The dynamical behavior of the solutions are analyzed by studying the figures of the exact solutions with different parameters. Finally, the conservation laws for the vcBKK equations are derived using the new conservation theorem, further enriching the study of the vcBKK equations.

This paper studies the soliton solutions of a class of variable-coefficient 2-coupled Schrödinger equations. Firstly, the integrability of the equation is tested by the Painlevé analysis method, and the specific constraint conditions for the equation under Painlevé integrability are derived. Secondly, the Riemann-Hilbert method and the Hirota bilinear method are respectively employed for analysis, and the N-soliton solution is derived via these two distinct approaches. For the Riemann-Hilbert method, the variable-coefficient model is transformed into a constant-coefficient form via variable replacement. The Riemann-Hilbert problem is then constructed based on the Lax pair, and the N-soliton solution expression is directly obtained by discussing the regular and non-regular cases. For the Hirota bilinear method, the bilinear equation in a functional form is directly obtained via rational transformation, and the N-soliton solution of the equation is derived through mathematical induction. Furthermore, to explore the dynamic behavior and evolution of these solutions, we present the time-dependent evolution diagrams of solitons via numerical simulation methods. On this basis, we conduct a more comprehensive analysis of the influence of several variable-coefficient functions on soliton propagation. The influence law of the function (beta (t)) on the corresponding physical quantities of solitons is also obtained.

This research analyzed the magnetic behavior of Penta-graphene-like nanostructures using Monte Carlo simulations and the Blume–Emery–Griffiths model. The study exclusively examines the effects of key parameters including linear exchange coupling (𝐽), biquadratic coupling (K), external magnetic fields (H), and crystal fields (D) on the blocking temperature (T_B) and phase transitions. The results demonstrate that an increase in biquadratic coupling from K = 0.5 to K = 2.0 significantly raises T_B, while a crystal field |D| >5 notably reduces the blocking temperature. The analysis reveals a phase transition threshold at T = 2.5-3.0, with characteristic shifts of the magnetic susceptibility peaks. These results establish quantitative relationships between interaction parameters and magnetic properties, thus providing control strategies to optimize material performance in high-density magnetic storage and spintronics applications.

The Rydberg blockade mechanism is a powerful tool for enabling deterministic entanglement in neutral-atom quantum computing and simulation. In this work, we investigate the coherent dynamics of a three-level atomic ensemble, where the highest energy level corresponds to a highly excited Rydberg state, and driven by two laser fields, incorporating detuning effects via an effective Hamiltonian that enforces the Rydberg blockade condition. First, we analyze the system’s eigen structure and derive conditions for the existence of a dark state. Then, to quantify entanglement generation, we compute the Fidelity with respect to a target Bell state and demonstrate that a gradient-free optimization of the single-atom detunings (Delta _1) and (Delta _2) can steer the system from the collective ground state into a high-Fidelity entangled superposition of excited and Rydberg levels. We validate this approach through time-domain simulations for both small ((N=2)) and mesoscopic ((N=10)) ensembles, achieving peak Bell-state fidelities exceeding 0.99 with appropriate detuning choices. Our results show that detuning control alone, without shaped pulses or adiabatic techniques, is sufficient to achieve fast and robust entanglement generation on experimentally relevant timescales. This strategy is scalable and relies solely on the spectral properties of the effective Hamiltonian, making it well-suited for extension to larger systems and more complex entangled targets.

In this work, we introduce an interesting method for determining the annihilation and creation operators in physical systems. This method is based on the Berezin integral mapping from the phase space of a system to the associated Hilbert subspace, and on the effect of the Thiemann complexifier on this mapping. Although the method is general, we apply it to two specific cases: a harmonic oscillator with phase space “(mathbb {C} simeq mathbb {R}^2)” , and a particle moving in a circle with phase space “(S^{1}times mathbb {R})”.

In this paper, an efficient bilinear neural network method (BNNM) is developed for the (2+1)-dimensional Benjamin-Bona-Mahony-Burgers (BBMB) equation. This method enables the comprehensive derivation of diverse solutions, including breather solutions, lump solutions, and lump-N-soliton solutions ((Nrightarrow infty)). By incorporating specific activation functions into a single hidden layer neural network model and employing symbolic computation software, exact solutions can be systematically constructed. Furthermore, the evolutionary behaviors and dynamic characteristics of these solutions are graphically illustrated through suitable parameter selections. The results presented in this study enhance our understanding of the solution structures and provide physical insights into the behavior of the model. These findings also contribute to the exploration of nonlinear wave phenomena in other scientific domains.