International Journal of Theoretical Physics最新文献

In this work, Asymptotic Iteration Method (AIM) is systematically employed to obtain quasi-exact analytical solutions of the Schrödinger equation for a one-dimensional general sextic oscillator which also includes a centrifugal term. This potential function has been previously discussed in the literature and quasi-exact eigenfunctions and eigenvalues of the corresponding quantum mechanical system have been investigated by means of the bi-confluent Heun equation and quasi-exact solvability approach. Alternatively, we achieve the energy eigenvalues in a closed form, which can be used to establish energy spectrum, for the case where none of potential parameters equals zero, in the present study. For reliability analysis of the analytical expression obtained, a numerical scheme based on AIM is further utilized within the arbitrary potential parameter regimes. Owing to this analytical expression, one will be able to see the effect of each potential parameters on the energy spectrum of the system.

In this work, we introduce a novel quantum correlation measure based on an affinity-induced quantum coherence framework to explore nonlocal effects arising from local quantum channels. Specifically, we define the correlation as the difference between the global bipartite coherence and the coherence of its marginal states, using quantum affinity as the coherence quantifier. We investigate this measure under the action of various local channels, including unitary operations, Lüders measurements, and weak measurements. Our analysis demonstrates that the proposed measure effectively distinguishes between product states and classical-quantum states, thereby serving as a faithful indicator of nonclassical correlations. Furthermore, we establish connections between the proposed measure and classical uncertainty, as well as quantum parameter estimation via Fisher information. Illustrative examples are provided using well-known two-qubit states to demonstrate the behavior of the correlation under different noisy quantum channels.

Quantum coherent entanglement was examined through optical interference in 1991. It has become a critical resource in quantum information technology. Research has shown a mutual relationship between coherence and entanglement, highlighting the connection between these two fascinating phenomena in quantum physics. However, understanding many-body coherent entanglement is a challenge, especially since the underlying mechanism of the Einstein–Podolsky–Rosen (EPR) paradox remains unresolved, dating back to 1935. This paper explores a new framework for understanding quantum coherent entanglement through the lens of complex adaptive systems (CAS). Using a nonlocal agent-based wave equation from financial theory, we define density momentum, density force, and density energy. This method allows us to establish a mathematical relationship among density energy, interaction energy, and linear potential. Utilizing the Hamilton–Jacobi equation initially employed by Schrödinger, we derived a nonlocal many-body wave equation, resulting in independent energy states and interaction-coherent entangled states. The pure interaction wave functions simplify many-body computations, improving our understanding of non-Gaussian distributions in complex quantum entanglement. Additionally, we identify a unified paradigm that connects the many-body wave equation with Schrödinger's wave equation. In conclusion, we justify strong correlation between two seperated parts in interaction-coherent entanglement through invariance or conservation of the interaction-coherent frequencies between the repulsive density force and the attractive restoring force within the inseparable states using probability, frequency, or color. Although requiring energy, the pure interaction-coherent entangled states can serve as high-quality resources, indicating potential applications in quantum many-body computation and quantum information technology.

We study the (de)localization properties of a quasi-exactly solvable (QES) sextic potential (V_{text {QES}}(x) = tfrac{1}{2}(x^6 + 2x^4 - 2(2lambda + 1)x^2)) as a function of the tunable parameter (lambda in [-tfrac{3}{4},6]). For the lowest states (n=0,1,2,3), variational wavefunctions are constructed that respect parity, have correct asymptotics, and admit analytical Fourier transforms. Energies agree with Lagrange-mesh and exact QES results with relative errors of order (10^{-8}) for (n=0,1,2) and (10^{-6}) for (n=3). We show that information-theoretic indicators (Shannon entropy, Kullback–Leibler and Cumulative Residual Jeffreys divergences) are more sensitive than variance-based measures in detecting tunneling transitions, symmetry breaking, and level pairing. The Beckner–Białynicki-Birula–Mycielski entropic uncertainty relation is verified across all (lambda), and trial densities are validated by divergences as small as (10^{-10}) from exact solutions. Importantly, while QES solvability allows for analytic benchmarking, many of the informational signatures identified here—such as entropy sensitivity and divergence-based detection of quasi-degeneracy—are generic to symmetric double-well systems and not restricted to the QES framework.

The evaluation of the charge radii, the correction to the Dashen’s theorem, and contributions of the box diagrams for the light-by-light scattering to the magnetic anomaly of the muon from the charged pions, charged kaons and the neutral kaons needs a reliable behaviour of the electromagnetic form factors of the latter particles in the space-like region. Recently with this aim existing experimental data have been used in this region, which, however seem not to be very reliable. Therefor in this paper we utilize a theoretical prediction of electromagnetic form factors of charged pions, kaons and neutral kaons behaviours in the space-like region by means of the Unitary and Analytic models, the parameters of which are fixed from transparent data in time-like region, obtained in the (e^{+}e^{-}) annihilation experiments. The resultant charge radii, the correction to the Dashen’s theorem and contributions of the box diagrams for the light-by-light scattering in this way are then compared with results of other authors, in order to reveal to what extent the unreliable experimental behaviours of the corresponding electromagnetic form factors in the space-like region influenced the calculated physical quantities.

In this article, the Klein-Gordon equation, a model for nonlinear wave propagation in high-energy nuclear settings, is studied in terms of bifurcation, chaotic dynamics, and solitary wave solutions. The study use the planar dynamical system technique to investigate self-interactions within the wave field, with a focus on phenomena including radiation transport, plasma oscillations, and neutron wave propagation in fission and fusion. Solitons, wave steepening, and energy localization all crucial elements in nuclear explosions and plasma instabilities—are produced by these interactions. In quantum mechanics and quantum field theory, spin-0 particles are described by the Klein-Gordon equation, a basic relativistic wave equation that serves as the foundation for scalar field theory and the quantization of such fields. It is specifically significant in general relativity, where it is extended to curved spacetime to analyze scalar fields under gravitational influences. It is also commonly used in modeling free particles and studying wave propagation in many physical systems. A key mathematical model for investigating the characteristics and solutions of partial differential equations in both physics and applied mathematics, the equation also has traditional uses in characterizing vibrating systems and nonlinear wave phenomena. The analysis employs a range of advanced dynamical tools, including phase diagrams, Lyapunov exponents, Poincaré maps, time series, bifurcation diagrams, fractal dimensions, strange attractors, recurrence plots, and return maps, revealing both chaotic and quasi-periodic behaviors. A perturbation term is introduced to further enrich the system’s dynamics, yielding a variety of complex patterns. Soliton solutions such as dark, bright, kink, anti-kink, periodic, and singular solitons are derived using the novel Improved Auxiliary Problem Mapping technique. Enhanced sensitivity analysis, supported by 3D, 2D, stream, density, contour, and phase trajectory visualizations, demonstrates the model’s dependence on initial conditions and showcases its capability in modeling more intricate phenomena. A stability analysis of the solitary wave solutions using the Hamiltonian technique confirms the consistency of the results, which are systematically organized for clarity. This study not only advances our understanding of nonlinear wave dynamics and soliton behavior but also highlights the model’s applicability to high-energy nuclear physics, providing valuable insights into the role of shock waves and turbulence in energy dissipation and structural changes in complex media.

In this paper, we study the exact solutions for bound states of the position-dependent mass Schrödinger equation with a nonlinear harmonic oscillator in the framework of the extended uncertainty principle by using the concept of the generalized supersymmetric approach. The bound state energy eigenvalues and the corresponding wave functions expressed in terms of modified Hermite polynomials are obtained analytically. Furthermore, special cases of interest in this problem are deduced, and our results are found to agree well with the results reported in the literature.

Only a few issues, such as the hydrogen atom, the harmonic oscillator, and square wells, provide an exact solution to the Schrödinger equation. Approximation methods can be used when exact solutions to the Schrödinger equation cannot be obtained. We develop a semiclassical Wentzel–Kramers–Brillouin (WKB) approximation for the quaternionic time-independent Schrödinger equation with purely imaginary quaternionic potentials. Using a generalized ansatz, the wavefunction separates into a real phase and a reduced quaternionic amplitude. The resulting equations yield a transport law that ensures the conservation of the probability current and a dispersion relation for the phase. Two formal solutions arise, but only one reduces correctly to the complex WKB limit, resolving the apparent multivaluedness of the quaternionic wavefunction. The formalism predicts corrections to semiclassical quantities at order (V_2^2 + V_3^2), leading to modified momenta, tunneling probabilities, and quantization conditions. In interferometric setups, these corrections manifest themselves as phase shifts and visibility reductions. The consistency with complex quantum mechanics, together with identifiable predictions, establishes the quaternionic WKB approximation as a foundation for future theoretical and experimental studies.

Nonlinear wave models have been widely researched in several relevant scientific disciplines, including theoretical physics, applied mathematics, and plasma physics, over the last 60 years. This research article focuses on deriving several analytical solutions and introduces newly constructed solitonic forms for a nonlinear (3+1)-dimensional evolution equation. The Generalized Exponential Rational Integral Function (GERIF) method is a recently advanced method to investigate exponential, trigonometric, hyperbolic, logarithmic, and inverse function solutions. We visualize these solutions through 3-dimensional (3D), contour, and contour plots to enhance their comprehensibility. These graphical representations show soliton-form solutions, including lumps, peakons, solitons, periodic lumps, periodic peakons, periodic solitons, solitonic wave-patterns, cone shapes, etc. These applications significantly enhance the quality and significance of our work, showcasing the utility of the newly introduced GERIF method. By bridging the gap between theoretical physics, plasma physics, and physical applications, this work presents an entirely new point of view on the evolving multi-soliton and multi-peakon patterns. These findings open the door for future developments in plasma waves and wave propagation while deepening our understanding of complex systems. The obtained forms of graphical representations have not been thoroughly studied in soliton theory up to this point. This research is the first ever to investigate the dynamics of newly generated solutions in plasma physics, nonlinear dynamics, and theoretical physics, incorporating multi-solitons, multi-peakons, and other solitons.