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Abstract: An Erratum to this paper has been published: https://doi.org/10.1134/S0040577922120108 PubDate: 2023-11-01

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Abstract: We classify semidiscrete equations of hyperbolic type. We study the class of equations of the form $$\frac{du_{n+1}}{dx}=f\biggl(\frac{du_{n}}{dx},u_{n+1},u_{n}\biggr),$$ where the unknown function \(u_n(x)\) depends on one discrete ( \(n\) ) and one continuous ( \(x\) ) variables. The classification is based on the requirement that generalized symmetries exist in the discrete and continuous directions. We consider the case where the symmetries are of order \(3\) in both directions. As a result, a list of equations with the required conditions is obtained. PubDate: 2023-11-01

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Abstract: We derive a general expression for the trace of the energy–momentum tensor \(T \kern0.9pt\overline{\vphantom{T}\kern6.0pt}\kern-6.9pt T \) -deformed field theories using a dynamical change of coordinates. Then we perform a dimensional reduction of the bilinear \(T \kern0.9pt\overline{\vphantom{T}\kern6.0pt}\kern-6.9pt T \) operator and obtain a new \(T \kern0.9pt\overline{\vphantom{T}\kern6.0pt}\kern-6.9pt T \) -like deformation of the quantum mechanics of free nonrelativistic fermions and the interacting Calogero–Sutherland system. The deformation leads to a change in the energy spectrum but does not affect the eigenfunctions. Furthermore, an expression for the deformed classical Lagrangian is obtained. We also study the correspondence between the two-dimensional Yang–Mills theory and the Calogero–Sutherland system in the presence of the deformation. PubDate: 2023-11-01

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Abstract: We continue the study of the B-Toda hierarchy (the Toda lattice with the constraint of type B), which can be regarded as a discretization of the BKP hierarchy. We introduce the tau function of the B-Toda hierarchy and obtain bilinear equations for it. Examples of soliton tau functions are presented in explicit form. PubDate: 2023-11-01

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Abstract: A solution of the scattering problem is obtained for the Schrödinger equation with the potential of induced dipole interaction, which decreases as the inverse square of the distance. Such a potential arises in the collision of an incident charged particle with a complex of charged particles (for example, in the collision of electrons with atoms). An integral equation for the wave function is constructed for an arbitrary value of the orbital momentum of relative motion. By solving this equation, an exact integral representation for the \(K\) -matrix of the problem is obtained in terms of the wave function. This representation is used to analyze the behavior of the \(K\) -matrix at low energies and to obtain comprehensive information on its threshold behavior for various values of the dipole momentum. The resulting solution is applied to study the behavior of the scattering cross sections in the electron–positron–antiproton system. PubDate: 2023-11-01

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Abstract: A system of equations with a quadratic nonlinearity in the electric field potential and temperature is proposed to describe the process of heating of semiconductor elements of an electrical board, with the thermal and electrical “breakdowns” possible in the course of time. For this system of equations, the existence of a classical solution not extendable in time is proved and sufficient conditions for a unique global-in-time solvability are also obtained. PubDate: 2023-11-01

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Abstract: We study the negative-order modified Korteweg–de Vries equation and show that it can be integrated by the inverse spectral transform method. We determine the evolution of the spectral data for the Dirac operator with periodic potential associated with a solution of the negative-order modified Korteweg–de Vries equation. The obtained results allow applying the inverse spectral transform method for solving the negative-order modified Korteweg–de Vries equation in the class of periodic functions. Important corollaries are obtained concerning the analyticity and the period of a solution in spatial variable. We show that a function constructed using the Dubrovin–Trubowitz system and the first trace formula satisfies the negative-order modified Korteweg–de Vries equation. We prove the solvability of the Cauchy problem for the infinite Dubrovin–Trubowitz system of differential equations in the class of three-times continuously differentiable periodic functions. PubDate: 2023-11-01

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Abstract: By systematically studying the infinite degeneracy and constants of motion in the Landau problem, we obtain a central extension of the Euclidean group in two dimension as a dynamical symmetry group, and \(Sp(2,\mathbb{R})\) as the spectrum generating group, irrespective of the choice of the gauge. The method of group contraction plays an important role. Dirac’s remarkable representation of the \(SO(3,2)\) group and the isomorphism of this group with \(Sp(4,\mathbb{R})\) are revisited. New insights are gained into the meaning of a two-oscillator system in the Dirac representation. It is argued that because even the two-dimensional isotropic oscillator with the \(SU(2)\) dynamical symmetry group does not arise in the Landau problem, the relevance or applicability of the \(SO(3,2)\) group is invalidated. A modified Landau–Zeeman model is discussed in which the \(SO(3,2)\) group isomorphic to \(Sp(4,\mathbb{R})\) can arise naturally. PubDate: 2023-11-01

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Abstract: The spherical and parabolic wave functions are calculated for the generalized MIC–Kepler system in the continuous spectrum. It is shown that the coefficients of the parabola–sphere and sphere–parabola expansion are expressed in terms of the generalized hypergeometric function \(_{3}F_2(\ldots\mid 1)\) . The quantum mechanical problem of scattering in the generalized MIC–Kepler system is solved. PubDate: 2023-11-01

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Abstract: We consider a one-dimensional Ising model (chain) with the the nearest-neighbor interaction and with a random nonmagnetic dilution. We find the exact free energy of such a chain as a function of the impurity concentration, temperature, and the external magnetic field. In the case of antiferromagnetic interaction in the chain, we find the specific magnetization, the mean value of the product of neighboring spins, and the entropy as functions of these parameters. We study the residual system entropy. PubDate: 2023-11-01

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Abstract: We provide an integrable discretization of the modified Korteweg–de Vries–sine Gordon equation. The discrete form is a coupled system and is derived via the Cauchy matrix approach by introducing suitable discrete plane wave factors. Solutions and a Lax pair are constructed in this approach. The dynamics of some solutions are illustrated. The modified Korteweg–de Vries–sine Gordon equation is recovered in the continuum limit. PubDate: 2023-11-01

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Abstract: The \(\mathcal N=2\) superconformal algebra characters have to exhibit modular invariance in order to be appropriately applied in quantum superstring theories. The nonunitary characters are given by higher-level Appell functions and different kinds of Jacobi theta functions are involved within their algebraic structures. Evaluating their \(\mathcal T\) -modular invariance appears to be quite simple, but verifying their \(\mathcal S\) -modular invariance entails a serious mathematical physics exploration. In this regard, we use a new vocabulary for Jacobi theta functions, namely “spectral theta functions,” which allows us to come up with the \(\mathcal S\) -modular transformation of nonunitary (nontrivial) \(\mathcal N=2\) characters for the central charge \(c=3(1-2p/u)\) , where \((u,p)\) is a pair of coprime positive integers. PubDate: 2023-11-01

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Abstract: We use the concept of gauge transformations in the proof of the invariance of the statistics of zero-vorticity lines in the case of the inverse energy cascade in wave optical turbulence; we study it in the framework of the hydrodynamic approximation of the two-dimensional nonlinear Schrödinger equation for the weight velocity field \(\mathbf u\) . The multipoint probability distribution density functions \(f_n\) of the vortex field \(\Omega=\nabla\times\mathbf u\) satisfy an infinite chain of Lundgren–Monin–Novikov equations (statistical form of the Euler equations). The equations are considered in the case of the external action in the form of white Gaussian noise and large-scale friction, which makes the probability distribution density function statistically stationary. The main result is that the transformations are local and conformally transform the \(n\) -point statistics of zero-vorticity lines or the probability that a random curve \(\mathbf x(l)\) passes through points \(\mathbf x_i\in\mathbb R^2\) for \(l=l_i\) , \(i=1,\dots,n\) , where \(\Omega=0\) , is invariant under conformal transformations. PubDate: 2023-11-01

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Abstract: We obtain second-order nonlinear differential equations (and the associated Bäcklund transformations) with an arbitrary analytic function of the independent variable. These equations (which are not of Painlevé type in general) under certain constraints imposed on an arbitrary analytic function can be reduced, in particular, to the second, third or fourth Painlevé equation. We consider the properties of the Bäcklund transformations for the second-order nonlinear differential equations generated by two systems of two first-order nonlinear differential equations with quadratic nonlinearities in derivatives of the unknown functions. PubDate: 2023-11-01

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Abstract: We study the \((3+1)\) -dimensional stochastic potential Yu–Toda–Sasa–Fukuyama equation (SPYTSFE) forced in the Itô sense by a multiplicative Wiener process. To obtain trigonometric, hyperbolic, and rational SPYTSFE solutions, we use the Riccati–Bernoulli sub-ODE and He’s semiinverse methods. The SPYTSFE may explain many exciting physical phenomena because it relates to nonlinear waves and solitons in dispersive media, plasma physics, and fluid dynamics. We show how the Wiener process affects the exact SPYTSFE solutions by introducing several 2D and 3D graphs. PubDate: 2023-11-01

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Abstract: We consider an \(XYZ\) spin chain within the framework of the generalized algebraic Bethe ansatz. We study scalar products of the transfer matrix eigenvectors and arbitrary Bethe vectors. In the particular case of free fermions, we obtain explicit expressions for the scalar products with different number of parameters in two Bethe vectors. PubDate: 2023-10-01

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Abstract: We study random velocity effects on a two-species reaction–diffusion system consisting of three reaction processes \(A+A\to(\varnothing,A)\) , \(A+B\to A\) . Using the field theory perturbative renormalization group, we analyze this system in the vicinity of its upper critical dimension \(d_{\mathrm c}=2\) . A velocity ensemble is generated by means of stochastic Navier–Stokes equations. In particular, we investigate the effect of thermal fluctuations on the reaction kinetics. The overall analysis is performed in the one-loop approximation and possible macroscopic regimes are identified. PubDate: 2023-10-01

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Abstract: We develop the BRST–BV approach to the construction of the general off-shell Lorentz covariant cubic, quartic, and \(e\) -tic interaction vertices for irreducible higher-spin fields on \(d\) -dimensional Minkowski space. We consider two different cases for interacting integer higher-spin fields with both massless and massive fields. The deformation procedure to find a minimal BRST–BV action for interacting higher-spin fields, defined with help of a generalized Hilbert space, is based on the preservation of the master equation in each power of the coupling constant \(g\) starting from the Lagrangian formulation for a free gauge theory. For illustration, we consider the construction of local cubic vertices for \(k\) irreducible massless fields of integer helicities, and \(k-1\) massless fields and one massive field of spins \(s_1, \dots, s_{k-1}, s_k\) . For a triple of two massless scalars and a tensor field of integer spin, the BRST–BV action with cubic interaction is explicitly found. In contrast to the previous results on cubic vertices, following our results for the BRST approach to massless fields, we use a single BRST–BV action instead of the classical action with reducible gauge transformations. The procedure is based on the complete BRST operator that includes the trace constraints used in defining the irreducible representation with a definite integer spin. PubDate: 2023-10-01

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Abstract: We estimate one-loop electroweak radiation corrections to the process of dilepton production in the photon fusion channel during hadron collisions for the Large Hadron Collider (LHC) experimental program of the study of the Drell–Yan process. We numerically and comprehensively analyze the effects of electroweak corrections to cross sections and the forward–backward asymmetry in a wide kinematic region, including for the CMS LHC experiment in the Run3/HL mode, which corresponds to superhigh energies and invariant masses of the lepton pair. PubDate: 2023-10-01

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Abstract: We investigate the thermodynamic properties and Hawking–Page phase transition of a black hole in the Schwarzschild–anti-de Sitter–Beltrami (SAdSB) spacetime. We discuss the Beltrami, or inertial, coordinates of the anti-de Sitter (AdS) spacetime. A transformation between noninertial and inertial coordinates of the AdS spacetime is formulated in order to construct a solution of a spherical gravitating mass and other physical quantities. The Killing vector is determined and used to calculate the event horizon radius of this black hole. The SAdSB black hole entropy and temperature are determined by the Noether charge method; the temperature is shown to be bounded by the AdS radius. Similarly, the Smarr relation and the first law of black hole thermodynamics for the SAdSB spacetime are formulated. The Gibbs free energy and heat capacity of this black hole are calculated and the phase transition between small and large black holes is considered. A first-order phase transition between the thermal AdS spacetime and the large-black-hole phase is also investigated and the Hawking–Page temperature is computed and compared with that of the Schwarzschild-anti-de Sitter black hole. PubDate: 2023-10-01