International Journal of Theoretical Physics最新文献

The Neural Network Quantum State (NNQS) approach offers a novel way to solve problems in quantum physics. Although this technique has been successful in addressing various issues, further research is needed to understand its full potential and limitations. In this study, we propose a neural network-based solution for the spinless particle within the Schwarzschild metric for three coordinate systems and compare it with the solution of the Klein–Gordon–Fock equations with a Coulomb potential. Our approach bridges the gap between analytic and numerical methods, improving the quality and usefulness of future studies in this field.

We extend stratified black hole evaporation by systematically analyzing the quantum extremal surfaces (islands) associated with each interior layer and their dynamical role in information recovery. In this framework, every concentric shell supports its own quantum extremal surface, which becomes dominant at a distinct Page time. This layered island structure gives rise to a generalized staircase Page curve, where entropy decreases occur sequentially as deeper layers are reconstructed. We solve for these layer-resolved quantum extremal surfaces explicitly in a multi-layer Jackiw–Teitelboim gravity model and show that the entanglement wedge of the Hawking radiation advances inward one layer at a time. We further generalize the analysis to multiple radiation channels and compute the full multipartite entropy using inclusion–exclusion formulas. Each radiation subsystem exhibits its own stepwise Page curve, while the total multipartite entropy remains finite even after all individual entropies vanish. This residual contribution signals an irreducible secret-sharing entanglement structure in the final radiation state, characterized by a nonzero Markov gap. Our results extend the island prescription to nested, multi-layer geometries and reveal new patterns of holographic redundancy and multipartite entanglement in black hole evaporation.

This work investigates the spherically symmetric solutions for the N-dimensional pressureless Navier-Stokes equations with density-dependent viscosity and damping term. By employing the method of variable separation, we systematically derive a set of reduced equations characterizing such solutions with spherical symmetry. Our analysis yields several new classes of exact spherically symmetric solutions featuring velocity (varvec{u}) with nonlinear form of spatial variable, particularly demonstrating solutions of the form (varvec{u}(varvec{x}, t)=c(t) |varvec{x}|^alpha varvec{x} (alpha ne 0) ). Notably, these solutions exhibit nonlinear form of the spatial variable - representing, to our knowledge, the first nonlinear-form solutions construction for this class of pressureless Navier-Stokes systems with density-dependent viscous and damping effects. The developed methodology demonstrates potential applicability for investigating exact spherically symmetric solutions across other nonlinear partial differential equations, suggesting promising avenues for extending this analytical approach.

We present a comparative study of noninteger-n Slater-type functions (NISTFs) and conventional Slater-type functions (CSTFs) for modeling electron density properties of neutral atoms from He to Xe using minimal basis sets. Radial moments (langle {r}^{k}rangle) (k = –2 to + 4), the Quantum Similarity Index (QSI), and information-theoretical measures—Kullback–Leibler (KL) divergence and Relative Fisher Information (RFI)—were used to assess accuracy against near Hartree–Fock quality reference densities. NISTFs consistently outperformed CSTFs across 291 of 318 moments. They also showed smoother QSI trends and lower divergence values in KL and RFI analyses. These results demonstrate the effectiveness of NISTFs in representing electron density within the Hartree–Fock-Roothaan method. Additionally, we observed a notable relationship between QSI deviations and total energy errors for both NISTF and CSTF basis sets.

We study Lie point symmetry structure of generalized nonlinear wave equations of the form (Box u=F(x, u, nabla u)) where (Box ) is the ((n+1))-dimensional space-time wave (or d’Alembert) operator, (xin mathbb {R}^{n+1}) ((nge 2)). We find the equivalence groups of this class and its subclass where the first order derivatives are absent. We then determine the symmetry group as a special case of the equivalence from the invariance requirement of the nonlinearity F leading to the symmetry condition involving F. As an application we solve this condition for some specific cases of F to build physically important equations like conformally-invariant nonlinear wave and Euler–Poisson–Darboux equation. Canonical forms for allowable symmetries are also studied.

As is well known, transformations play a crucial role in studying nonlinear evolution equations—especially when constructing their analytical solutions. On one hand, transformations can simplify these equations; solving the simplified versions then allows us to obtain the solutions of the original equations. On the other hand, establishing transformations between different equations (or between different solutions of the same equation) enables further derivation of a series of new solutions for the original equations. This paper studies a stochastic Riemann wave equation. Specifically, new transformations are introduced to simplify the original equation into a couple of integer-order nonlinear evolution equations, followed by constructing various types of multi-wave mixed solutions or nonlinear superposition solutions via several efficient algorithms. Additionally, by establishing new auto Bäcklund transformations for the equation, a series of distinct new solutions can be further derived based on the previously obtained ones. These results provide important insights into stochastic wave phenomena and offer analytical tools for understanding wave behavior in physical contexts such as nonlinear optics and quantum mechanics, while advancing methods for stochastic nonlinear differential equations.

This work presents a deterministic scheme for the teleportation of a single qutrit state, held by the sender Alice, using maximally entangled two-qutrit states as resource channels. These states have been constructed from symmetric and anti-symmetric bases by Leslie, Devin and Lynn (LDL). Leveraging the higher information capacity of qutrits compared to qubits, we employ these nine distinct two-qutrit entangled channels by LDL, for our protocol. For each channel, explicit unitary operations at the receiver Bob’s end are derived, ensuring perfect recovery of the unknown qutrit state, initially in possesion of the sender Alice, after the sender performs joint measurements on her qutrits and communicates the outcomes through a classical channel. The proposed framework confirms teleportation with unit fidelity, thereby extending conventional teleportation schemes beyond qubits into higher-dimensional systems. This not only enriches the available toolkit for quantum communication but also highlights the utility of structured entangled states in advancing quantum information processing. The results open new avenues for secure and efficient quantum networks, higher-dimensional cryptographic schemes, and the design of novel quantum algorithms, while laying the groundwork for experimental realizations of deterministic qutrit teleportation.

Quantum devices flown in Low Earth Orbit (LEO) are exposed to hostile environments where cosmic rays, solar radiation, and long-lived material defects induce temporally correlated noise. In such scenarios, the well-known Markovian Lindblad formalism may be insufficient for correlated noise scenarios, as the memory less bath assumption is broken. In this work, we bridge formal non-Markovian frameworks (Nakajima–Zwanzig and Time-Convolutionless master equations) with an accessible stochastic method based on the Ornstein–Uhlenbeck (OU) process, resulting in a tractable surrogate model of colored noise with finite correlation time. We solve the corresponding stochastic Schrödinger equation and recover reduced dynamics through ensemble averaging. Numerical simulations reveal three characteristic signatures of non-Markovian dynamics: (i) partial protection and revivals of coherence, (ii) trajectory-dependent fluctuations in fidelity, and (iii) information backflow as quantified by the Breuer–Laine–Piilo measure. For the simulated parameters, the OU model extends the effective coherence time by a factor of approximately 1.5 compared to the Markovian case, while maintaining higher fidelity for longer times. These findings indicate both the benefits and challenges of non-Markovian effects for space-based quantum systems. They provide practical insight for quantum communication (e.g. satellite QKD), sensing, and computation in orbit, and suggests non-Markovian noise modeling as a promising approach for designing robust and radiation-hardened quantum technologies in space.

We present a new spectral-theoretic derivation of the density of states ( rho left( lambda right) ) for the sublaplacian operator on the Heisenberg group (mathbb {H}^{n}). Our method exploits a fundamental connection between this operator and the magnetic Laplacian operator in ( mathbb {C}^{n}), linked via a Fourier transform. While the resolvent kernel for the sublaplacian operator is established from a prior work (and whose consistency with Folland’s fundamental solution is a key validation of its form), our core contribution lies in the direct application of the associated spectral density kernel (dE_{lambda }/dlambda ) to obtain (rho left( lambda right) =gamma _{n}lambda ^{n}, gamma _{n}>0) is a constant. This approach provides an independent, (L{{}^2})-spectral alternative to the harmonic analysis techniques used by Strichartz (J. Fourier Anal. Appl. 18, 626–659, 2012) to find the integrated density of states, whose derivative confirms our result. Additionally, we provide a general formula for the integrated density of states of the magnetic Laplacian operator in (mathbb {C}^{n}), extending Nakamura’s one-dimensional result (Nakamura, J. Funct. Anal. 179(1), 136–152, 2001). This work highlights the practical utility of the connection between these two operators, demonstrating that the spectral theory of the Heisenberg sublaplacian operator can be effectively advanced by transferring results from the well-studied context of magnetic Hamiltonians in (mathbb {C} ^{n}).

This study extends the class of highly nonlinear Schrödinger equations by incorporating the resonant and cubic derivative terms, alongside infusing the quadrupled power-law nonlinearity term. This inclusion of terms is introduced in the present study, in addition to the proposal of an optimal analysis methodology. The modified Kudryashov method is employed for solitonic analysis. Further, the study constructs various sorts of exponential-logarithmic solutions that recast to singular and dark solitonic expressions, in addition to the construction of dissimilar supplementary optical solitons that pave the way for parametric analysis for optimal optical transmission of waves in a nonlinear medium. Remarkably, the reported graphical illustrations, which serve as the basis for the parametric analysis, indicated that the inclusion of the resonant term in the model proliferates the wave dynamics in the medium. At the same time, the incorporation of the cubic derivative term must vanish for the integrability condition to hold. Moreover, various effects have been noted by both the model’s and method’s parameters, besides the provision of the solitons’ stability and modulation instability analyses. In the end, the study recommends further study in the realm of highly nonlinear complex-valued evolution equations with emphasis on the contemporary fields of relevance, like optical communication, quantum field theory, and the design and analysis of fluid and waveguide structures, among others.