International Journal of Theoretical Physics最新文献

In this study, we focus on the numerical solutions of the Stochastic Gross-Pitaevskii Equation (SGPE), a critical tool for modelling Bose-Einstein Condensates (BEC) in low-temperature regimes. Using a finite difference scheme, we investigate the dynamics of ultra-cold atomic systems under various external potentials and stochastic influences. The potentials explored include harmonic, periodic, Gaussian, magnetic, dipole, and asymmetric (step-like) scalar potentials, as well as systems with attractive and repulsive interactions. Stability and consistency of the numerical approach are demonstrated through Von-Neumann analysis and mean square consistency tests. Simulations incorporating Ornstein-Uhlenbeck noise provide detailed insights into condensate behaviour under these diverse potentials, highlighting the intricate interplay of stochastic effects and interparticle interactions. Our findings offer a comprehensive numerical framework and results that contribute to advancing both theoretical and experimental physics. The trends we quantify (peak reduction and broadening under noise) align qualitatively with observations in trapped-BEC experiments, underscoring the practical applicability of our numerical framework.

In this paper, we consider the evolution of coherent Bell-like states under a cyclic unitary non-local transformation and compare the geometric phase and linear entropy of these states. We show that in some cases, the geometric phase can indicate entanglement. However, we will provide examples of both separable and entangled states for which, unlike linear entropy, the geometric phase is unable to indicate the entanglement property.

Quantum cognition has made it possible to model human cognitive processes very effectively, revealing numerous parallels between the properties of conceptual entities tested by the human mind and those of microscopic entities tested by measurement apparatuses. The success of quantum cognition has also made it possible to formulate an interpretation of quantum mechanics, called the conceptuality interpretation, which ascribes to quantum entities a conceptual nature similar to that of human concepts. The present work fits into these lines of research by analyzing a cognitive version of single-slit, double-slit, and triple-slit experiments. The data clearly show the formation of the typical interference fringes between the slits, as well as the embryos of secondary fringes. Our analysis also shows that while quantum entities and human concepts may share a same conceptual nature, the way they manifest it in specific contexts can be quite different. This is also evident from the significant deviation from zero observed for the Sorkin parameter, indicating the presence of strong irreducible third-order interference contributions in human decision.

Unitary metaplectic representations of the group (varvec{SL}_{textbf{2}}(mathbb {Z}_{textbf{2}^{varvec{n}}})) are necessary to describe the time evolution of (textbf{2}^{varvec{n}})-dimensional quantum systems, such as systems involving n qubits. It is shown that in order for the metaplectic property to be fulfilled, an increase in the dimensionality of the involved n-qubit Hilbert spaces, from (textbf{2}^{varvec{n}}) to (textbf{2}^{textbf{2}{varvec{n}}}), is necessary. Thus we construct the general matrix form of such representations based on the magnetic translations of the diagonal subgroup (varvec{HW}_{textbf{2}{varvec{n}}} otimes varvec{HW}_{textbf{2}{varvec{n}}}). Comparisson with other approaches on this problem of the literature are discussed.

The black hole information paradox arises from Hawking’s semiclassical analysis showing that evaporating black holes emit only thermal radiation, leading to apparent loss of information. Unitarity demands that the radiation’s von Neumann entropy follow a Page curve, first rising and then eventually falling to zero. Here we propose a model in which the black hole interior is stratified into concentric layers of distinct quantum degrees of freedom. We apply the quantum extremal surface (island) prescription to compute the entanglement entropy of the Hawking radiation in this layered geometry. We find a staircase-shaped Page curve: after an initial rise, the entropy reaches successive plateaus and then drops each time a new island, associated with an inner layer, becomes dominant. Each drop corresponds to the transfer of information from one layer to the radiation, yielding sequential purification of the black hole. This multi-step Page curve realizes unitary evaporation in discrete stages and implies a cascade of entanglement-wedge reconstructions that progressively include deeper layers. These results highlight how black hole microstructure can be unveiled through entanglement dynamics, with broad implications for holography and semiclassical gravity.

This work investigates the cosmological implications of the Extended Bose–Einstein Condensate (EBEC) equation of state within the framework of f(Q, C) gravity, aiming to provide deeper insight into the nature of dark matter and dark energy. The EBEC model, characterized by the equation of state (p = alpha rho + beta rho ^2), unifies classical dark matter with its quantum ground state properties. A linear model (f(Q,C) = -psi left( frac{Q}{Q_0}right) + delta C) (Model 1) and a nonlinear model (f(Q,C) = -psi left( frac{Q}{Q_0}right) ^2 + delta C) (Model 2) are investigated. We constrain the parameters of both models with CC, BAO and Pantheon supernova datasets via MCMC techniques. The best-fit values for (H_0), (eta), and (beta) for each model lie within observational bounds. Our analysis reveals a consistent late-time transition from deceleration to acceleration, with the present-day equation of state parameter (omega _0) asymptotically approaching (-1), resembling a cosmological constant. The SEC is violated in both models across all redshifts, indicating the presence of repulsive gravity, while the other conditions are preserved, ensuring physical viability. The evolution of the statefinder parameters shows trajectories passing through the (Lambda)CDM fixed point ((r=1, s=0)), transitioning from a quintessence-like phase to a future phantom regime. Both models exhibit stable behavior with a sound speed squared (0< c_s^2 < 1) throughout cosmic history. The estimated ages of the Universe from the datasets are approximately 13.47–13.57 billion years for Model 1 and 13.49–13.59 billion years for Model 2. These results demonstrate that both linear and nonlinear forms of the f(Q, C) gravity model, when coupled with EBEC dark matter, offer viable and physically consistent descriptions of the Universe’s late-time accelerated expansion.

In this work, we present a comprehensive study of the (3+1)-dimensional nonlinear Korteweg–de Vries (KdV)-type hierarchy equation using a hybrid methodology that integrates the bilinear neural network method (BNNM) and symbolic computation. Leveraging the powerful characteristics of BNNM, we first construct a single-hidden-layer network to obtain exact breather, lump, and interaction wave solutions. The model’s architecture effectively encodes the bilinear form of the presenting equation, allowing effective extraction of nonlinear wave structures. To extend the representational capacity and capture more intricate dynamical behaviors, we then implement a deeper neural architecture particularly, a "4-2-2-1" multi-layer network model. This setup presents superior flexibility in handling complex interactions between solitary waves and localized structures. In contrast to the traditional analytical techniques, the BNNM framework suggests a dual advantage: it preserves the mathematical rigor of bilinear soliton theory while harnessing the universal approximation capabilities of neural networks. Through symbolic computation integrated with the neural outputs, we ensure exact algebraic satisfaction of the target PDE. This technique not only enhances accuracy and computational efficiency but also allows the discovery of diverse wave phenomena including breathing solitons, interference waves, and hybrid lump-stripe structures that are difficult to detect via classical techniques. The findings advance the understanding of KdV-type systems and provide a promising direction for data-driven soliton theory and high-dimensional nonlinear modeling.

In this paper, modulation instability and modulated wave patterns are developed in an anharmonic monoatomic chain. The linear stability with small perturbations is used to establish an expression for the modulation instability growth rate, which permits pointing out stable and unstable zones under the effects of the nearest-neighbor interaction. It is demonstrated that the variation of the anharmonic term can affect the modulation instability bands and reduce the unstable zone. Throughout the numerical simulation, we have pointed out rogue waves and different forms of the trains of pulse to confirm the existence of modulation instability. Using the semidiscrete multi-scale method, we have derived the nonlinear Schrödinger equation from where we have displayed the periodic structures and solitonic waves in the allowed phonon band. Using the nonlinear supratransmission phenomenon, we point out the localized waves and trains of pulse in the forbidden gap where the driven amplitude is considered above the supratransmission threshold. Chaotic behavior is observed to emerge within a specific range of propagation time. These findings may open new avenues for further research on delocalized waves in monoatomic chains.

In quantum secret sharing research, the construction of communication efficient schemes constitutes an important research direction. Recently, a class of communication efficient quantum threshold secret sharing schemes was proposed. However, the investigation was limited to analyzing communication costs during the reconstruction phase. This paper focuses on quantum secret sharing schemes based on multi-particle entangled states, constructing a practical and efficient quantum secret sharing scheme. Performance analysis of the scheme shows that by optimizing the communication mechanism and resource allocation strategy, when the combiner recovers the secret by accessing any authorized set of size (varvec{d}_{varvec{i}}), with the increase of (varvec{d}_{varvec{i}}), the communication cost in the reconstruction phase is effectively reduced, and the quantum communication efficiency is significantly improved. Finally, we prove that the protocol is secure under intercept-and-resend attacks, collusion attacks, entangle-and-measure attacks, and Trojan horse attacks.

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.