International Journal of Theoretical Physics最新文献

In this study, we first take the integer order model and then extend it using the fractional operator due to the benefits of the fractional derivative. Next, we discuss the SEIB model in a fractional framework with the Atangana-Baleanu-Caputo derivative and examine its dynamics. The existence and uniqueness of model solutions are investigated using fixed-point theory. After that, we apply the fractal-fractional notation with the Atangana-Baleanu derivative to the SEIB model and find that it has a unique solution. Different fractal and fractional order values are used to depict graphical representations. We also compare the considered operators using two distinct numerical schemes with various fractional order values. Further we conclude the fractal-fractional technique is superior to the fractional operator.

This study examines the effects of Newtonian heating along with heat generation, and thermal radiation on magnetohydrodynamic Casson fluid over a vertical plate. At the boundary, the Newtonian heating phenomena has been employed. The problem is split into two sections for this reason: momentum equation and energy equations. To transform the equations of the given model into dimensionless equations, some particular dimensionless parameters are defined. In this article, generalized Fourier’s law and the recently proposed Caputo Fabrizio fractional operator are applied. The corresponding results of non-dimensional velocity and heat equations can be identified through the application of Laplace transform. Moreover, Tzou’s algorithm as well as Stehfest’s algorithm is implemented to recognize the inverted Laplace transform of heat and momentum equations. Finally, a graphical sketch is created using Mathcad 15 software to demonstrate the results of numerous physical characteristics. It has been reported that the heat and velocity drop with rising Prandtl number values, whereas the fluid’s velocity has been seen to rise with increasing Grashof number values. Additionally, current research has shown that flow velocity and temperature increase with rising values of a fractional parameter.

The present study investigates the dynamics of a string cloud within the framework of f(R)-gravity theory. We analyze the properties of the string cloud spacetime governed by f(R) gravity, deriving expressions for the Ricci tensor, scalar curvature, and the equation of state. We find a delicate balance between the particle density (rho ) and string tension (lambda ) during the quintessence era. Additionally, employing the Ricci soliton as our metric, we determine conditions for the soliton’s behavior under different vector fields. We derive modified Poisson and Liouville equations and explore the formation of a black hole and trapped surfaces outside it in the context of a shrinking Ricci soliton within a string cloud spacetime under f(R)-gravity. Finally, by considering the gradient Ricci soliton, we establish conditions on the particle density (rho ) for the spacetime to undergo contraction, remain steady, or expand.

This paper reviews the history of the conformal extension of Galilean symmetry, now called Schrödinger symmetry. In the physics literature, its discovery is commonly attributed to Jackiw, Niederer and Hagen (1972). However, Schrödinger symmetry has a much older ancestry: the associated conserved quantities were known to Jacobi in 1842/43 and its Euclidean counterpart was discovered by Sophus Lie in 1881 in his studies of the heat equation. A convenient way to study Schrödinger symmetry is provided by a non-relativistic Kaluza-Klein-type “Bargmann” framework, first proposed by Eisenhart (1929), but then forgotten and re-discovered by Duval et al. only in 1984. Representations of Schrödinger symmetry differ by the value (z=2) of the dynamical exponent from the value (z=1) found in representations of relativistic conformal invariance. For generic values of z, whole families of new algebras exist, which for (z=2/ell ) include the (ell )-conformal Galilean algebras. We also review the non-relativistic limit of conformal algebras and that this limit leads to the 1-conformal Galilean algebra and not to the Schrödinger algebra. The latter can be recovered in the Bargmann framework through reduction. A distinctive feature of Galilean and Schrödinger symmetries are the Bargmann super-selection rules, algebraically related to a central extension. An empirical consequence of this was known as “mass conservation” already to Lavoisier. As an illustration of these concepts, some applications to physical ageing in simple model systems are reviewed.

In this work, we provide new optical soliton structures of the Kadomtsev-Petviashvili equation in (3 + 1)-dimensional and the Jimbo-Miwa equation in (3 + 1)-dimensional together with some intriguing new analysis, chaotic phenomena, bifurcation properties, and sensitivity analysis. Since soliton structure with three analyses is a very interesting recent topic in nonlinear dynamics, we extract different chaotic structures, bifurcation analysis together with phase portrait and sensitivity of our mentioned nonlinear partial differential equations. Applications of the Kadomtsev-Petviashvili equation are in sonic waves, magneto sonic waves, superfluid, weakly nonlinear quasi-unidirectional waves, shallow water waves with weakly nonlinear restoring forces and frequency dispersion, plasma physics, etc. Advanced intellect could benefit from studying the Jimbo-Miwa equation, which addresses specific fascinating higher-dimensional waves in marine engineering, ocean sciences, various interesting physical structures in the areas of optics, acoustic, mathematical modeling, epidemics, circuit analysis, computational neuroscience, intergalactic modeling, etc. Due to the huge applications of the mentioned equations, there is a high demand to investigate with recently developed three analyses. Making use of the recently developed advanced strategy, the adaptive, compatible, further advanced closed-form solitary wave structures are harvested to the mentioned equations in the present manuscript. All these scientifically accomplished exact soliton structures, which take the forms of rational functions and trigonometric functions could assist in our comprehension of remarkable nonlinear challenging situations. In contrast to the present outcomes, our newly formed discoveries will exhibit unique features. The outcomes that were extracted confirm that the recommended technique is meticulously planned, intuitive, and advantageous for measuring the dynamic behavior of nonlinear evolution equations within contemporary science and technology.

The electromagnetic interaction, in reality, is screened at a distance, and thus, the screened or cut-off Coulomb potentials are considered to visualize the effect of screening in real situations. The exact analytical expressions for off-shell solutions and transition matrix are constructed for motion in Hulthén-modified rank-one separable potential via the differential equation approach to the problem. The off-shell transition matrix for the said potential has not yet been discussed in the literature. The usefulness of these expressions is examined through some model calculations.

Optical solitons are controlled and modified in a four level N-type atomic medium under the effect of cross Kerr nonlinearity. Significant control over optical solitons are reported with variation of driving fields and system parameters. The single and mixed types optical solitons are controlled for the first time with strength of applied driving fields in the medium. Single dark and bright optical solitons are achieved by fixing Rabi frequencies, detuning and phase of applied driving fields. The multi-peakon and periodic type optical solitons are also modified with strength of applied driving fields. Further more the mixed-types of optical solitons including dark-peakon, breather-periodic, multi-peakon-breather and multi-peakon-breather-periodic types optical solitons are investigated with the variation of control fields Rabi frequencies, detunings and decay rates. The modified single and mixed types optical solitons have potential application in soliton radar technology and sensors as well as communication technologies.

Quantum Private Queries (QPQ) is aimed to protect both user privacy and database security while executing database queries. In recent years, although many QPQ protocols based on Quantum Key Distribution (QKD) have been proposed, in most protocols, users’ measurement devices may suffer from detector-side-channel attacks initiated by dishonest database owners. To address this issue, we propose a new Measurement-Device-Independent (MDI) QPQ protocol. The protocol outsources all measurement operations to an impartial third party, effectively thwarting detector side-channel attacks. Furthermore, this protocol employs linear error correction codes to rectify the raw key, thereby mitigating security vulnerabilities in block query situations arising from repeated queries and communication errors. The protocol incorporates permutation-shift-addition operations to further obscure the information accessible to the user post error correction of the raw key. Compared to existing protocols, the proposed protocol has higher practicality and practical security.

Fluid dynamics cooperating with nonlinear science could describe many natural phenomena, e.g., the Boussinesq-Burgers-type equations for the shallow water waves. In this paper, as for the shallow water waves in a lake or near an ocean beach, we study a Boussinesq-Burgers system. Via the Hirota method and symbolic computation, we derive two sets of the bilinear forms, namely, transforming that Boussinesq-Burgers system into two sets of the bilinear form equations. Besides, we also create a set of the similarity reductions for that Boussinesq-Burgers system via the Clarkson-Kruskal direct method, simplifying that Boussinesq-Burgers system to a solvable ordinary differential equation. Our results rely on the variable coefficient in that Boussinesq-Burgers system. We hope that our results could be of some use for the future water-wave studies.

The heart of the light field theory at finite temperatures is the introduce of a thermal vacuum state, which is also the basis for studying the statistical properties of quantum light fields. Based on Takahashi and Umezawa's thermal chaotic field dynamics theory (TFD), this paper introduces a " fictitious mode" to represent the degrees of freedom of the thermal environment, then the thermal vacuum of the displaced thermal state (DTS) is proposed and constructed by the integration within an ordered product (IWOP) in the extended space, and we obtained the expected value of the photon number, fluctuation, second-order coherence, Wigner function. Finally, it is found that the photon number of the system is decreased at a rate of (kappa t) due to the interaction of the DTS with the surrounding thermal environment by calculating the photon number diffusion.