International Journal of Theoretical Physics最新文献

This paper presents a novel application of an extended tanh approach, termed the NITM (Novel Improved Tanh approach), for tackling the complex cubic nonlinear Schrödinger equation with a delta potential. This model serves as essential for the description of optical waveguides that contain localized defects. Through a unified computational framework, we derive a extensive family of exact analytical solutions, including trigonometric periodic waves, hyperbolic solitons, and solutions expressed in terms of Jacobi and Weierstrass elliptic functions, as well as rational forms. The NITM framework constitutes a significant extension of classical tanh-function methods by incorporating a more flexible ansatz structure, which proves highly effective in managing complex nonlinearities. All derived solutions are rigorously verified using symbolic computation in Maple. Furthermore, detailed graphical analyses illuminate the influence of critical parameters on wave propagation dynamics. As one of the first implementations of NITM in the scientific literature, this work not only demonstrates the method’s superior capability for generating a diverse spectrum of solutions with computational efficiency but also provides new insights into nonlinear wave phenomena. These findings confirm NITM as a robust tool for the analysis of nonlinear partial differential equations in mathematical physics.

A difficulty in quantum logic is the well-known arbitrariness in choosing a binary operation for conditional among three principal candidates called the Sasaki, the contrapositive Sasaki, and the relevance conditional, mainly chosen from syntactical grounds. A fundamental problem remains to clarify their semantical differences manifest in operational concepts in quantum theory. Here, we attempt such an analysis through quantum set theory, developing models of quantum set theory built upon quantum logics with those three conditionals, each of which defines different quantum logical truth-value assignment for set theoretical statements. We show that each of them satisfies the transfer principle to determine the truth values of theorems of the ZFC set theory and defines the internal reals bijectively corresponding to the observables of the quantum system under consideration. Then, the truth values of their equality relations are identical irrespective of the chosen conditionals. Interestingly, however, their order relations exhibit a strong dependence on the specific conditional employed, while the order relation attains full truth value if and only if Olson’s spectral order relation holds. We further characterize the order relation in terms of experimentally accessible relations for outcomes of successive projective measurements of the corresponding observables, showing that each choice has its own operational meaning with symmetry between the Sasaki and the contrapositive Sasaki conditionals, in contrast to the majority view that favors the Sasaki conditional. Our findings reveal that quantum set theory yields empirically testable predictions concerning state-dependent binary relations between quantum observables, thereby extending Born’s probabilistic interpretation from propositions to relations.

This research gives a full investigation of magnetic properties and stability of a nested borospherene (B₄₀) nanostructure based on Monte Carlo simulations through the Blume–Capel model. The model is given as core–shell structure with mixed spins (3/2,1) with antiferromagnetic core–shell exchange coupling (j_CS). The study rigorously investigates the influence of the most significant parameters-crystal field (d), internal core coupling (j_C), interfacial coupling (j_CS), and temperature (t)-on magnetism, i.e., ground-state phase diagrams and complex magnetization plateaus creation. The results have the overall magnetization show six plateaus, the reversal process being regulated by two key fields (h_C1 and h_C2) and a saturation field (h_S). Anisotropy (|d|) is observed to be the most dominating controlling parameter of magnetic hardness because it linearly increases h_C2 and h_S. Contrarily, the increase of the core internal stiffness (j_C) surprisingly reduces h_S and helps the subsequent magnetic reversal, and the interfacial coupling (|j_CS|) actually controls the order and plateau’s structure. Furthermore, thermal fluctuations, which are introduced by high temperature, more and more smooth and minimize the transitions. The above observations gain profound knowledge about the intrinsic magnetic stability mechanisms and transition characteristics in borospherene-derived nanostructures and therefore contain limitless prospects for future utilization in nanomagnetics and spintronics.

A quantum ring is considered in a rotating frame in the presence of an external magnetic field. The energy levels and wave functions of the system are analytically derived by solving the Schrödinger equation. Then, an analytical expression is derived for the coefficient of direct interband light absorption (ILA). Applying the expression, the threshold frequency of absorption (TFA) is analytically derived. This frequency is calculated for different parameters such as quantum ring radius, external magnetic field, and angular frequency of the rotating frame. According to the results, we found that the system shows a frequency in petahertz (PHz) range which can be used in wireless communications, industrial manufacturing environments, disinfecting water, food, medical equipment, explosives warehouses, and underwater scenarios. The TFA in the rotating frame is higher than the frequency in the rest frame. Also, this frequency is increased by enhancing the magnetic field and QR radius.

This paper investigates the magnetic behavior of C₆₀ and (C₆₀)₂ fullerene nanostructures through Monte Carlo simulations of the Blume-Emery-Griffiths model. To analyze the blocking temperatures (T_B) of both structures under various conditions, the research substitutes carbon atoms with their spin-1 counterparts. The research shows that due to greater exchange interactions and reduced surface effects, (C₆₀)₂ surpasses C₆₀ in possessing higher blocking temperature. Significant consideration is given to important parameters such as the magnetization and susceptibility, the inflicted magnetic field, crystal field, linear and biquadratic exchange couplings. These findings pertain to the fabrication of these materials and devices, while also shedding light on the dynamics of fullerene system magnetization.

We deal with the analogous of the so-called Quantum Markov Chains for Fermi systems (i.e. the models whose fundamental fields enjoy the Canonical Anti-commutation Relations), and discuss their main properties. Since the involution and the product highly differ from those of the usual tensor product, the positivity of the involved operators and functionals, not automatically satisfied, is a very delicate question. As a consequence, the positivity should be checked directly for the specific models under consideration. Therefore, we analyse some pivotal cases, providing examples which go beyond the simpler ones already studied in literature. As an interesting result, we prove that the symmetric states, that is those which are invariant under the natural action of the group of all finite permutations, are described in terms of particular Quantum Markov Chains.

We present the on-shell regular, Jost, and physical solutions for the Deng-Fan plus Graz separable potential in its maximal reduced form. To validate our analytical framework, we apply these solutions to low-energy nucleon-nucleus scattering, where our calculated physical observables align closely with established theoretical and experimental findings, reinforcing the accuracy and significance of our approach.

In this paper, we mainly investigate the dynamical behaviors of the interaction of solitons, breathers and rogue waves on the nonzero constant background for the (1+1)-dimensional Ito equation. By employing the Hirota bilinear method, we derive the N-soliton solution and further investigate its degenerate behaviors. As a result, various kinds of localized wave solutions, including breather, rogue wave and their hybrid structure, are derived. What’s more, we demonstrate the interaction features between different localized wave solutions by controlling parameters. These results are of great significance for understanding nonlinear wave dynamics.

The antiferromagnetic (AF)-ferromagnetic (FM) spin-3/2 Blume-Capel (BC) model is constructed on the Bethe lattice (BL) and then examined in terms of the exact recursion relations (ERR) to calculate its phase transition properties by mapping the phase diagrams of the model. They are obtained on the crystal field-temperature planes for given values of the external magnetic field and probability parameter giving the strength of the AF interaction over the FM one, or vice versa, on the square lattice. The lattice is divided into sublattices A and B to include the effects of the AF interactions. It is found that the model gives very interesting critical points and behaviors in terms of the combinations of the multi-phase lines in the form of either the first- or second-order type.

The Lane-Emden equation, a nonlinear second-order ordinary differential equation, plays a fundamental role in theoretical physics and astrophysics, particularly in modeling the structure of stellar interiors. Also referred to as the polytropic differential equation, it describes the behavior of self-gravitating polytropic spheres. In this study, we present a novel approach to the solution of the eigenvalue problem which arises when considering the Lane-Emden equation for (n = 0, 1, 2, 3, 4) using Physics-Informed Neural Networks (PINNs). The novelty of this work is that, we not only solve the Lane-Emden equation via PINNs but we also determine the eigenvalue, r, which is the stellar radius. Hyperparameter tuning was conducted using Bayesian optimization in the Optuna framework to identify optimal values for the number of hidden layers, number of neurons, activation function, optimizer, and learning rate for each value of n. The results show that, for (n = 0, 1), PINNs achieve near-exact agreement with theoretical eigenvalues (errors < (0.000806%)). While for more nonlinear cases, (n = 2, 3) and (n=4), PINNs yield errors below (0.0009%) and (0.05%) respectively, validating their robustness.