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Semiclassical Asymptotics and Particle-Antiparticle Interactions for the Dirac Equations with Abruptly Varying 4-Potential 具有突变4势的Dirac方程的半经典渐近性和粒子-反粒子相互作用
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-02-09 DOI: 10.1134/S1061920824040010
A.I. Allilueva, A.I. Shafarevich
{"title":"Semiclassical Asymptotics and Particle-Antiparticle Interactions for the Dirac Equations with Abruptly Varying 4-Potential","authors":"A.I. Allilueva,&nbsp;A.I. Shafarevich","doi":"10.1134/S1061920824040010","DOIUrl":"10.1134/S1061920824040010","url":null,"abstract":"<p> Using Maslov’s canonical operator in the Cauchy problem for a Dirac equation, we consider the asymptotics of the solution of the Cauchy problem in which the potential depends irregularly on a small parameter. </p><p> <b> DOI</b> 10.1134/S1061920824040010 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 4","pages":"577 - 586"},"PeriodicalIF":1.7,"publicationDate":"2025-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143373289","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Caricature of Hydrodynamics for the Harmonic Crystal Coupled to a Klein–Gordon Field 耦合于克莱因-戈登场的谐波晶体流体力学漫画
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-02-09 DOI: 10.1134/S1061920824040034
T.V. Dudnikova
{"title":"Caricature of Hydrodynamics for the Harmonic Crystal Coupled to a Klein–Gordon Field","authors":"T.V. Dudnikova","doi":"10.1134/S1061920824040034","DOIUrl":"10.1134/S1061920824040034","url":null,"abstract":"<p> We consider a Hamiltonian system consisting of the Klein–Gordon field coupled to an infinite harmonic crystal. The dynamics of the coupled system is invariant with respect to the space translations in <span>(mathbb{Z}^d)</span>, <span>(dge1)</span>. We study the Cauchy problem and assume that the initial date is a random function. We introduce the family of initial probability measures <span>({mu_0^varepsilon,varepsilon &gt;0})</span> depending on a small parameter <span>(varepsilon)</span> and slowly varying on the linear scale <span>(1/varepsilon)</span>. For times of order <span>(varepsilon^{-kappa})</span>, <span>(kappa&gt;0)</span>, we study the asymptotics of the distributions of the random solution as <span>(varepsilonto0)</span>. In particular, we show that, for <span>(kappa=1)</span> and <span>(kappa=2)</span>, the limiting covariance is governed by the hydrodynamic equations of the Euler and Navier–Stokes type, respectively. </p><p> <b> DOI</b> 10.1134/S1061920824040034 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 4","pages":"606 - 621"},"PeriodicalIF":1.7,"publicationDate":"2025-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143373295","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Some Properties and Applications of Operator Continued (J)-Fractions 算子连通性的若干性质及应用(J) -分数
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-02-09 DOI: 10.1134/S1061920824040125
A. Osipov
{"title":"On Some Properties and Applications of Operator Continued (J)-Fractions","authors":"A. Osipov","doi":"10.1134/S1061920824040125","DOIUrl":"10.1134/S1061920824040125","url":null,"abstract":"<p> We consider a certain class of infinite continued fractions such that their elements are bounded operators in a Hilbert space. They can be regarded as analogs of <span>(J)</span>-fractions related to the classical moment problem and the theory of Jacobi operators. To each of these operator <span>(J)</span>-fractions there corresponds a band operator generated by three-diagonal infinite matrix which entries coincide with the elements of this continued fraction. Using the theory of such band operators, we establish the basic properties of the continued fractions under consideration: their expansion algorithm, a criterion for existence of this expansion, and the uniqueness theorem. Also we establish the convergence (at a geometric rate) of an operator <span>(J)</span>-fraction outside the numerical range of the corresponding band operator to the Weyl function of the latter. We show how these results can be applied for solving quadratic operator equations. </p><p> <b> DOI</b> 10.1134/S1061920824040125 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 4","pages":"737 - 757"},"PeriodicalIF":1.7,"publicationDate":"2025-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143373311","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Series of Spectral Gaps for the Ganeshan–Pixley–Das Sarma Model Ganeshan-Pixley-Das Sarma模型的一系列谱隙
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-02-09 DOI: 10.1134/S1061920824040046
A. Fedotov, K. Sedov
{"title":"A Series of Spectral Gaps for the Ganeshan–Pixley–Das Sarma Model","authors":"A. Fedotov,&nbsp;K. Sedov","doi":"10.1134/S1061920824040046","DOIUrl":"10.1134/S1061920824040046","url":null,"abstract":"<p> We study a one-dimensional quasiperiodic difference Schrödinger operator with a potential obtained by restricting a certain meromorphic function to the integer lattice. Assuming that the coupling constant is sufficiently small, we asymptotically describe a series of intervals contained in spectral gaps, their centers, and lengths. The lengths of these intervals decrease exponentially as their number increases, and the rate of their decrease is determined by the distance from the poles of the potential to the real axis. </p><p> <b> DOI</b> 10.1134/S1061920824040046 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 4","pages":"622 - 644"},"PeriodicalIF":1.7,"publicationDate":"2025-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143373286","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Landis Conjecture in a Cylinder 论圆柱体中的兰迪斯猜想
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-02-09 DOI: 10.1134/S1061920824040058
N.D. Filonov, S.T. Krymskii
{"title":"On the Landis Conjecture in a Cylinder","authors":"N.D. Filonov,&nbsp;S.T. Krymskii","doi":"10.1134/S1061920824040058","DOIUrl":"10.1134/S1061920824040058","url":null,"abstract":"<p> The equation <span>(- Delta u + V u = 0)</span> in the cylinder <span>(mathbb{R} times (0,2pi)^d)</span> with periodic boundary conditions is considered. The potential <span>(V)</span> is assumed to be bounded, and both functions <span>(u)</span> and <span>(V)</span> are assumed to be <i> real-valued</i>. It is shown that the fastest rate of decay at infinity of nontrivial solution <span>(u)</span> is <span>(Oleft(e^{-c|w|}right))</span> for <span>(d=1)</span> or <span>(2)</span>, and <span>(Oleft(e^{-c|w|^{4/3}}right))</span> for <span>(dge 3)</span>. Here <span>(w)</span> stands for the axial variable. </p><p> <b> DOI</b> 10.1134/S1061920824040058 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 4","pages":"645 - 665"},"PeriodicalIF":1.7,"publicationDate":"2025-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143373288","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
McLaughlin’s Inverse Problem for the Fourth-Order Differential Operator 四阶微分算子的McLaughlin反问题
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-02-09 DOI: 10.1134/S1061920824040022
N.P. Bondarenko
{"title":"McLaughlin’s Inverse Problem for the Fourth-Order Differential Operator","authors":"N.P. Bondarenko","doi":"10.1134/S1061920824040022","DOIUrl":"10.1134/S1061920824040022","url":null,"abstract":"<p> In this paper, we revisit McLaughlin’s inverse problem, which consists in the recovery of the fourth-order differential operator from the eigenvalues and two sequences of norming constants. We prove the uniqueness for solution of this problem for the first time. Moreover, we obtain an interpretation of McLaughlin’s problem in the framework of the general inverse problem theory by Yurko for differential operators of arbitrary orders. An advantage of our approach is that it requires neither the smoothness of the coefficients nor the self-adjointness of the operator. In addition, we establish the connection between McLaughlin’s problem and Barcilon’s three-spectra inverse problem. </p><p> <b> DOI</b> 10.1134/S1061920824040022 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 4","pages":"587 - 605"},"PeriodicalIF":1.7,"publicationDate":"2025-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143373349","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Moment Representations of Fully Degenerate Bernoulli and Degenerate Euler Polynomials 完全退化伯努利多项式和退化欧拉多项式的矩表示
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-02-09 DOI: 10.1134/S1061920824040071
D. S. Kim, T. Kim
{"title":"Moment Representations of Fully Degenerate Bernoulli and Degenerate Euler Polynomials","authors":"D. S. Kim,&nbsp;T. Kim","doi":"10.1134/S1061920824040071","DOIUrl":"10.1134/S1061920824040071","url":null,"abstract":"<p> Recently, the degenerate hyperbolic functions are studied in connection with the degenerate Bernoulli and degenerate Euler numbers which were introduced by Carlitz. The aim of this paper is to derive moment representations of the fully degenerate Bernoulli and degenerate Euler polynomials associated with the Laplace random variable with parameters <span>((a,b)=(0,1))</span>. In addition, we obtain the product expansions for the functions which are degenerate versions of <span>(frac{sinh t}{t})</span> and <span>(cosh t)</span>. We also obtain some new identities involving the fully degenerate Bernoulli and degenerate Euler numbers by using series expansions for certain degenerate hyperbolic functions. </p><p> <b> DOI</b> 10.1134/S1061920824040071 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 4","pages":"682 - 690"},"PeriodicalIF":1.7,"publicationDate":"2025-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143373281","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Absence of a Propagation Front in the Cauchy Problem for a Certain Integro-Differential Equation with a Rabotnov Kernel 一类带Rabotnov核的积分-微分方程Cauchy问题中传播前沿的不存在性
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-02-09 DOI: 10.1134/S1061920824040137
I.V. Romanov, A.S. Shamaev
{"title":"On the Absence of a Propagation Front in the Cauchy Problem for a Certain Integro-Differential Equation with a Rabotnov Kernel","authors":"I.V. Romanov,&nbsp;A.S. Shamaev","doi":"10.1134/S1061920824040137","DOIUrl":"10.1134/S1061920824040137","url":null,"abstract":"<p> The Cauchy problem on the real axis for the Gurtin–Pipkin equation with the Rabotnov kernel is considered. For some special case, it is proved that there is no propagation front in this problem. </p><p> <b> DOI</b> 10.1134/S1061920824040137 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 4","pages":"758 - 761"},"PeriodicalIF":1.7,"publicationDate":"2025-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143373312","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Extension of Unitary Characters from the Radical of a Connected Locally Compact Group to a One-Dimensional Pure Pseudorepresentation of the Group 连通局部紧群根上的酉字到群的一维纯伪表示的推广
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-02-09 DOI: 10.1134/S1061920824040149
A.I. Shtern
{"title":"Extension of Unitary Characters from the Radical of a Connected Locally Compact Group to a One-Dimensional Pure Pseudorepresentation of the Group","authors":"A.I. Shtern","doi":"10.1134/S1061920824040149","DOIUrl":"10.1134/S1061920824040149","url":null,"abstract":"<p> We prove necessary and sufficient conditions that an ordinary unitary character on the radical of a connected locally compact group admits an extension to a locally bounded finally precontinuous one-dimensional pure pseudorepresentation of the group. </p><p> <b> DOI</b> 10.1134/S1061920824040149 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 4","pages":"762 - 764"},"PeriodicalIF":1.7,"publicationDate":"2025-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143373313","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Localized Chern Character and the index of Elliptic Operators Associated with Discrete Groups 与离散群相关的椭圆算子的局域陈氏特征与索引
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-02-09 DOI: 10.1134/S1061920824040174
H.H. Abbas, A.Yu. Savin
{"title":"Localized Chern Character and the index of Elliptic Operators Associated with Discrete Groups","authors":"H.H. Abbas,&nbsp;A.Yu. Savin","doi":"10.1134/S1061920824040174","DOIUrl":"10.1134/S1061920824040174","url":null,"abstract":"<p> Given an action of an infinite discrete group on a smooth manifold, we construct an equivariant Chern character in cyclic cohomolgy of the crossed product for equivariant vector bundles over fixed point submanifolds of torsion elements in the group. We use this Chern character to obtain an index formula for nonlocal elliptic operators associated with the group action. </p><p> <b> DOI</b> 10.1134/S1061920824040174 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 4","pages":"785 - 790"},"PeriodicalIF":1.7,"publicationDate":"2025-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143373382","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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