International Journal of Theoretical Physics最新文献

This study addresses the challenge of derivig exact and soliton solutions for nonlinear evolution equations, which are essential for understanding complex phenomena in science, applied mathematics, and mathematical physics. Nonlinear evolution equations such as the ubiquitous Korteweg-de Vries equation and the Hirota-Ramani equation were studied due to their significant applications in modeling wave propagation, fluid dynamics, optics, plasma physics, and nonlinear dynamical systems. The modified simple equation method was employed, a strong method known for its consistency, efficiency, and effectiveness in deriving traveling wave solutions. Using this method, we obtained various solution types, including bell-shaped solitons, anti-bell-shaped solitons, kink-shaped solutions, pulse-shaped solitons, and soliton solutions. These results enhance our ability to predict system behavior under diverse conditions and extend the understanding of nonlinear systems. The novelty of this work lies in the improved applicability and performance of the modified simple equation method compared to existing methods, offering a more comprehensive framework for analyzing nonlinear evolution equations and advancing prior research in the field.

The subsets of Dicke states are highly entangled symmetric states known as the dihedral (D_{8})- symmetric states having the robust entanglement properties. In this work, we propose a quantum teleportation protocol for teleporting an arbitrary two-qubit state, a Bell-state and a Bell-like state using (D_{8})-symmetric entangled states as channel. The quantum circuits for the proposed teleportation protocol have been implemented on the IBM quasm-simulator and the results obtained confirm the successful execution of the protocol. In addition, the quantum circuit for an arbitrary two-qubit state has also been run on the real 127-qubit IBM Eagle quantum processor. Furthermore, by performing the quantum state tomography, the arbitrary two-qubit teleported state has been reconstructed at the Bob’s end with a 0.65 fidelity. The effects of three different noise types—amplitude damping, phase-flip, and bit-flip—on the proposed teleportation protocol have also been investigated. Additionally, a security study of the protocol against both internal and external attacks has been conducted.

We set the criteria under which superposition of causal order can be incorporated into quantum walks. In particular, we show that only periodic quantum walks or those with at least one disorder exhibit Superposition of causal order under the action of ‘quantum switch’. We exemplify our results with a simple example of two-period discrete-time quantum walks. In particular, we observe that periodic quantum walks exhibit causal asymmetry pertaining to the dynamics of the reduced coin state: the dynamics are more non-Markovian for one temporal order than the other. We also note that the non-Markovianity of the reduced coin state due to indefiniteness in causal order tends to match the dynamics of a particular temporal order of the coin state. We substantiate our results with numerical simulations.

In this study, the analytical eigensolutions of the radial Schrödinger equation with a point-like global monopole under the combined Manning-Rosen potential and screened Coulomb self-interaction potential has been investigated. The Greene-Aldrich approximation was used to overcome the centrifugal barrier which allows for the derivation of the energy and wave function in closed form. The solution of the energy and wave function were applied to investigate the scattering phase shift and thermodynamics function variations with topological defect parameter, quantum numbers and temperature, respectively. The results reveal that the energy eigenvalues and wave function amplitudes are influenced by the quantum numbers and the topological defect parameters. The shift in energy eigenvalues observed are caused by the particle collisions that exist in the system. The scattering phase shifts were found to be sensitive to the rotational quantum numbers and topological defect values. The thermodynamic plots exhibit high dependency on the temperature and topological defect parameters considered. Specific observation is the Schottky anomaly which exists uniquely for the topological defect values at low temperatures. Our results agree with occurrences in physical phenomenon, as recorded in literatures.

The time-regularized long-wave equation is pivotal in understanding diverse wave dynamics, such as shallow water waves, pressure waves in liquids and gas bubbles, ion-acoustic waves in plasma, and nonlinear transverse waves in magnetohydrodynamics. The analysis is initiated by deriving the infinitesimal generators of the Lie group symmetries, followed by constructing a commutator table and adjoint table to study the algebraic structure of the equation’s symmetries. Using this symmetries, the time-regularized long-wave equation is systematically reduced and solved for invariant solutions associated with each symmetry. These solutions give insight into the inherent properties of the system and wave behavior. The extended hyperbolic function method is employed to derive exact solutions to the simplified versions of the time-regularized long-wave equation. This method enhances the solution process by generating soliton solutions including dark, singular, bright and periodic-singular solutions. To illustrate their behavior of obtained solutions, graphical representations are given by using different values of parameters. A comprehensive bifurcation analysis is also conducted to explore the qualitative changes in the dynamics of system, while the Hamiltonian structure of the equation is constructed to investigate its conservation properties. The study also investigates the phase portraits of the system to offer a visual interpretation of the solution trajectories in phase space. Finally, the modulation instability of the time-regularized long-wave equation through linear stability analysis is analyzed to provide a clearer understanding of the conditions that lead to the onset of instability in wave propagation.

This study investigates the two-dimensional Dirac oscillator in (2+1)-dimensional spacetime under the influence of a perpendicular magnetic field, focusing on specific transitions in the magnetic quantum numbers m(varvec{>0}) and m(varvec{<0}). These transitions are characterized by the exchange of chiral creation and annihilation operators, which define two distinct directions associated with the magnetic field, termed right and left operators. We explore the behavior of spin-polarized electron vortices through these operators, applying the Jaynes-Cummings (JC) and Anti-Jaynes-Cummings (AJC) models to analyze quantum transitions. Utilizing the rotating wave approximation, we perform rotational coupling transformations (varvec{T_{pm }}) and counter-rotating transformations (varvec{L_{pm }}), leading to the derivation of the transformed Hamiltonians (varvec{H_{DOAJC}^{L_{pm }}}) and (varvec{H_{DOJC}^{T_{pm }}}). These results provide a deeper understanding of the dynamics and coupling mechanisms in the Dirac oscillator influenced by a magnetic field.

We discuss the nonclassical properties of photon-subtracted compass states (PSCS). Nonclassical behavior is studied using various parameters like the Wigner function, squeezing, and photon statistical parameters like Mandel’s Q-function, second-order correlation function, Agarwal-Tara (A_3) criterion, and photon number distribution. Further analysis is being done to investigate the sub-Planck structures in the Wigner functions of these PSCS. We also show that the photon subtraction doesn’t cause the loss of sensitivity due to displacement of the states in phase space.

We investigate black hole solution within the framework of a generalized Chaplygin-Jacobi dark fluid background, focusing on perturbations and the greybody factor in this intriguing model. This model holds significance due to its characterization by two critical parameters (alpha ) and (beta ) which signify the deviation from the Schwarzschild black hole and the degree of anisotropy in the dark fluid respectively. We study the time evolution of the black hole by focusing on these key parameters, demonstrating that they significantly influence the damping and oscillation frequencies. Additionally, we evaluate the greybody factor bounds for the black hole under consideration. The key parameters (alpha ) and (beta ) significantly affect the bounds of the greybody factors, indicating that lower-frequency radiation can escape the black hole, while higher-frequency radiation is more effectively trapped. This highlights the substantial influence of (alpha ) and (beta ) on the characteristics of the black hole. Thus, we investigate the influence of these parameters on the optical properties of the black hole. By considering both static and infalling accretion models, we explore the impacts of (alpha ) and (beta ) on the black hole’s shadows and photon rings.

The Gross-Pitaevskii Equation (GPE), which belongs to the class of nonlinear Schrödinger equations is recognized for its applications in diverse fields such as Bose-Einstein Condensates and optical fiber. In this study, the dynamic behaviors of various wave solutions to the M-fractional nonlinear Gross-Pitaevskii equation are examined. Intriguing insights into the mechanisms regulating the intricate wave patterns of the model are offered through this investigation. To secure the solutions, including complex, bright, dark, combined, and singular soliton solutions, the Kumar-Malik method, the modified generalized exponential rational function method, and the generalized multivariate exponential rational integral function method are substantially applied. The fractional parametric effects on solitary waves are observed graphically. Moreover, the Galilean transformation is adopted, and bifurcation, sensitivity, chaotic behavior, 2D and 3D phase portraits, Poincaré maps, time series analysis, and sensitivity to multistability under different conditions are explored.

This is the second part of a pair of companion papers devoted to an analysis of Einstein’s fusion picture for light. While in the foregoing paper “An Actual Discusion of Einstein’s Early Fusion Picture for Photons and Classical Maxwell Fields” (referred to as Rieckers 2025) our conclusions ended with the historical ab initio motivation and mathematical elaboration of a multi-photon theory in Fock space, we now start from the non–separable C*-Weyl algebra gained by abstracting the Fock–represented Weyl algebra. To the rich state space of this antiliminary observable algebra we apply notions of a convex state space approach to identify sub–theories that cover classical field states (including the vacuum with classical zero–field), that are possibly decorated by photonic quantum noise. The main emphasis is laid on direct integrals over irreducible, disjoint representations of the C*-Weyl algebra, decomposing the effective photon theory into sectors. Certain limits of smeared central field operators suggest a mathematical realization of Einstein’s early photon notion consisting of an energy point surrounded by a local force field (respective wave function). Macroscopic classical Maxwell fields are gained by superposing the expectation values of products of those composite photon operators. The ontological status of the explicated photon notion is discussed. Connections to Einstein’s historic photon theory, summarized in Rieckers (2025), as well as to quantum optical applications are hinted at throughout the paper.