International Journal of Theoretical Physics最新文献

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.

At present, there are at least two set theories motivated by quantum ontology: Décio Krause’s quasi-set theory ((mathfrak Q)) and Maria Dalla Chiara and Giuliano Toraldo di Francia’s quasi-set theory (QST). Recent work [Jorge-Holik-Krause, 2023] has established certain links between QST and Pawlak’s rough set theory (RST), showing that both are strong candidates for providing a non-deterministic semantics of N matrices that generalizes those based on ZF. In this work, we show that the new atomless quasi-set theory (mathfrak {Q}^-), recently introduced to account for a quantum property ontology [Krause-Jorge, 2024], has strong structural similarities with QST and RST. We study the level of extensionality that each theory presents, its relation to the Leibniz principle and the rigidity property. We believe that developing common features among these three theories can motivate common fields of research. By revealing shared structures, the developments of each theory can have a positive impact on the others.

We present a comprehensive and technically rigorous analysis of the status of Birkhoff’s theorem in Jackiw–Teitelboim (JT) gravity, a paradigmatic two-dimensional model for studying semiclassical gravitational dynamics. While Birkhoff’s theorem is well established in four-dimensional general relativity–asserting the uniqueness and staticity of vacuum solutions under reflection symmetry remains subtle due to the absence of propagating gravitational degrees of freedom. In this work, we systematically investigate the space of symmetry under radially symmetric configurations in JT gravity using both conformal and Schwarzschild-like gauges. Through analytical techniques and integral transformations, we explore the conditions under which vacuum solutions remain time-independent, identifying classes of metric-dilaton configurations that either uphold or violate Birkhoff-type behavior. Our findings reveal that the theorem holds only in restricted cases, depending critically on the separability of the conformal factor and the structure of the dilaton potential. These results clarify longstanding ambiguities surrounding symmetry and dynamics in two-dimensional gravity and establish JT gravity as a controlled setting for probing the breakdown of classical gravitational theorems in lower-dimensional and holographic contexts. This analysis contributes to a deeper understanding of the interplay between symmetry, integrability, and geometry in quantum gravity and strongly coupled systems.

This study explores non-linear dynamics of a two two-level atoms quantum system interacting with a two-mode quantized cavity field under the influence of f-deformed centrosymmetric Kerr medium and Stark effect. The system Hamiltonian consists of intensity-dependent atom–field coupling, self- and cross-phase modulation due to Kerr nonlinearity, and Stark-induced shifts. Initially, the field modes are in coherent states, and atoms are in their ground states. For this system, quantum properties such as Von Neumann entropy, population inversion, fidelity, and Quantum Fisher information are analyzed to study entanglement dynamics and parameter sensitivity. Mandel Q parameter and Wigner function reveal non-classical photon statistics and quantum phase-space features, respectively. Entanglement of formation is also studied which quantifies the atom–field correlations. The calculated results show that Kerr nonlinearity enhances dynamical complexity and phase evolution but reduces coherence and entanglement strength. Further, Stark shift subtly changes the system by detuning energy levels. These insights aid in designing controllable quantum states for quantum information applications.

Quantum teleportation, utilizing pre-shared entanglement, plays a vital role in the secure transmission of quantum information. In this study, we explore the feasibility of single-qubit quantum teleportation in the presence of intrinsic decoherence, utilizing two dissimilar coupled qubits that exhibit quantum oscillations. Additionally, we explore quantum remote sensing at the destination of a single-qubit quantum teleportation process, employing quantum remote estimation to assess the teleported state using Quantum Fisher Information (QFI). Furthermore, we analyze the system’s dynamics within the current model by investigating non-Markovianity witnessed through the QFI, a critical aspect in quantum communication. By appropriately adjusting system parameters such as the Josephson energies of the qubits and the energy of the mutual coupling between qubits, quantum teleportation, and quantum remote sensing can be enhanced under quantum oscillations.

We propose and investigate a Yukawa model featuring a dynamical scalar field coupled to relativistic Luttinger fermions. Using the functional renormalization group (RG) as well as large-(N_{textrm{f}}) or perturbative expansions, we observe the emergence of an infrared attractive partial fixed point in all interactions at which all couplings become RG irrelevant. At the partial fixed point, the scalar mass parameter is RG marginal, featuring a slow logarithmic running towards the regime of spontaneous symmetry breaking. The long-range behavior of the model is characterized by mass gap formation in the scalar and the fermionic sector independently of the initial conditions. Most importantly, a large scale separation between the low-energy scales and the microscopic scales, e.g., a high-energy cutoff scale, is naturally obtained for generic initial conditions without the need for any fine-tuning. We interpret the properties of our model as a relativistic version of self-organized criticality, a phenomenon observed in specific statistical or dynamical systems. This entails natural scale separation and universal long-range observables. We determine nonperturbative estimates for the latter including the scalar and fermionic mass gaps.

The longstanding pursuit of unifying physical laws is dependent to new conceptual frameworks that can bridge classical and modern physics. In this study, we establish a novel approach based on the concept of General Energy Behavior (GEB) to reinterpret and unify fundamental thermodynamic principles. Here, while defining, supplementing and integrating all established materials regarding Energy Structure Theory (EST), we introduce and formally define two universal laws of energy behavior: the Preference Law, which describes the system’s tendency to retain energy in non-dynamic forms, and the Exchange Law, which governs the interaction between independent and dependent components of non-dynamic energies. These GEB laws aim to unify aspects of the first and second laws of thermodynamics and offer a structured perspective for analyzing energy exchange processes in physical systems. We derive the corresponding mathematical formulations and validate them using a generalized application of Borchers’ remarks on the second law of thermodynamics. The results suggest that GEB laws may offer a useful theoretical basis for future efforts toward unifying physical principles.

Secure multi-party computational geometry is a crucial application domain of secure multi-party computation. Existing secure multi-party computation geometry protocols suffer from inefficiency and insufficient resistance to quantum attacks in computational geometry tasks. Meanwhile, quantum computing offers new possibilities to address these challenges through its inherent superposition and entanglement properties. To address the single-point trust risk in existing quantum summation or multiplication protocols, we redesign workflows by delegating critical tasks (quantum state preparation and result announcement) to a semi-honest third party. This prevents the initiator from accessing intermediate results while preserving the quantum-resistant properties of the underlying primitives. Based on this optimized framework, we construct efficient quantum-secure computational geometry protocols, including a two-party distance protocol and a polyhedron volume protocol with reduced third-party involvement. To our knowledge, we also present the first protocol for multi-party polygon area computation in quantum settings. The correctness and efficiency are formally analyzed, while heuristic security arguments against specific attacks are provided under defined assumptions.

Exactly solvable models play an extremely important role in many fields of quantum physics. In this study, the Schrödinger equation is applied for a solution of a two–dimensional (2D) problem for two particles interacting via Kratzer, and modified Kratzer potentials. We found the exact bound state solutions of the two–dimensional Schrödinger equation with Kratzer–type potentials and present analytical expressions for the eigenvalues and eigenfunctions. The eigenfunctions are given in terms of the associated Laguerre polynomials. The analytical expressions for the eigenvalues and eigenfunctions obtained by using the standard method could be beneficial in various physical analyses, including the chemical dissociation energy of the lowest vibrational level and equilibrium internuclear separation of the diatomic molecule, and retrieval of the material parameters such as reduced exciton mass and screening length from measured exciton energies. We also report analytical expressions for expectation values for r and (r^2), and the range of strength parameter g for modified Kratzer potential for excitons in freestanding transition metal dichalcogenides that reproduce theoretical and experimental binding energies.

Bianchi type-I solutions to Einstein’s field equations (EFE) are well-known and are characterized with homogeneity and anisotropy. These spacetimes specify a generalization of the Friedmann-Lemaître-Robertson-Walker (FLRW) where the universe could not keep spatial-invariance in its dynamics of cosmological expansion or contraction posing an anisotropic expansion which tends to decay as the universe evolves resulting into the present-day nearly an isotropic cosmic structure. In the present study we explore the character of anisotropy in the framework of (fleft( R right)) gravity in shaping cosmological evolution. We envisage geometrically the anisotropy mimicking the role as an independent metric degree of freedom apart from the average scale factor contrary to the approach followed in the general relativity where the scale factor due to time-dependence leverages the anisotropy to be uniquely determined. In order to investigate how the anisotropy evolution takes place in an anisotropic spacetime within (fleft( R right))context, we analyze it through Ricci scalar R which could lead to computing the scale factor alongside the anisotropy contribution throughout the time cosmologically. Additionally, We find out the critical role of anisotropy in the analysis of models under consideration where it gets suppressed in the large-scale structure of the cosmic evolution of the universe. By applying the certain construction method specifically two possibly viable phases are explored-quasi-de Sitter as implied by exponential expansion during inflationary dynamics and contraction phase as required by bounce models resulting from power laws in the purview of ekpyrotic frameworks. Furthermore, We work out a connection in relation to nonlinear behavior and the interplay between R as spawned in anisotropic spacetime and the expression pertaining to the anisotropy in (fleft( R right)) gravity. The occurence of possible singularities in explored anisotropic scenarios with the growth of scale factors has also been discussed briefly. Finally, by indicating an anisotropic solution in (fleft( R right)) models we urge the need of designating both the average scale factor and the total anisotropy as functions of time.