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The Hankel determinant for a semiclassical Laguerre unitary ensemble, Painlevé IV and Heun equations 半经典拉盖尔单元集合的汉克尔行列式、Painlevé IV 和 Heun 方程
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-06-25 DOI: 10.1134/S0040577924060035
Dan Wang
{"title":"The Hankel determinant for a semiclassical Laguerre unitary ensemble, Painlevé IV and Heun equations","authors":"Dan Wang","doi":"10.1134/S0040577924060035","DOIUrl":"10.1134/S0040577924060035","url":null,"abstract":"<p> We analyze the asymptotic behavior of the Hankel determinant generated by a semiclassical Laguerre weight. For this, we use ladder operators and track the evolution of parameters to establish that an auxiliary quantity associated with the semiclassical Laguerre weight satisfies the Painlevé IV equation, subject to suitable transformations of variables. Using the Coulomb fluid method, we derive the large-<span>(n)</span> expansion of the logarithmic form of the Hankel determinant. This allows us to gain insights into the scaling and fluctuations of the determinant, providing a deeper understanding of its behavior in the semiclassical Laguerre ensemble. Moreover, we delve into the asymptotic evaluation of monic orthogonal polynomials with respect to the semiclassical Laguerre weight, focusing on a special case. In doing so, we shed light on the properties and characteristics of these polynomials in the context of the ensemble. Furthermore, we explore the relation between the second-order differential equations satisfied by the monic orthogonal polynomials with respect to the semiclassical Laguerre weight and the tri-confluent Heun equations or the bi-confluent Heun equations. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"219 3","pages":"913 - 932"},"PeriodicalIF":1.0,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503132","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 class of field equations for neutrinos with nonzero masses 一类非零质量中微子场方程
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-06-25 DOI: 10.1134/S0040577924060023
N. G. Marchuk
{"title":"A class of field equations for neutrinos with nonzero masses","authors":"N. G. Marchuk","doi":"10.1134/S0040577924060023","DOIUrl":"10.1134/S0040577924060023","url":null,"abstract":"<p> We introduce a new equation (a class of equations) to be considered as a candidate for the equation for a nonzero-mass neutrino. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"219 3","pages":"897 - 912"},"PeriodicalIF":1.0,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503133","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Simplifying the large-mass expansion of Feynman integrals 简化费曼积分的大质量展开
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-06-25 DOI: 10.1134/S0040577924060072
V. A. Smirnov
{"title":"Simplifying the large-mass expansion of Feynman integrals","authors":"V. A. Smirnov","doi":"10.1134/S0040577924060072","DOIUrl":"10.1134/S0040577924060072","url":null,"abstract":"<p> We show how the well-known large-mass expansion of Feynman integrals can be simplified to obtain more terms of the expansion in analytic form. Expansion of two-loop four-point Feynman integrals that contribute to the <span>(H to ggg)</span> process is used as an example. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"219 3","pages":"986 - 991"},"PeriodicalIF":1.0,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141514123","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 hierarchy of the nonlocal nonlinear Schrödinger equation with self-consistent sources and dynamics 具有自洽源和动力学的非局部非线性薛定谔方程的层次结构
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-06-25 DOI: 10.1134/S0040577924060047
Qi Li, Qiu-yuan Duan
{"title":"A hierarchy of the nonlocal nonlinear Schrödinger equation with self-consistent sources and dynamics","authors":"Qi Li,&nbsp;Qiu-yuan Duan","doi":"10.1134/S0040577924060047","DOIUrl":"10.1134/S0040577924060047","url":null,"abstract":"<p> A hierarchy of the nonlocal nonlinear Schrödinger equation with self-consistent sources is introduced. The physically significant nonlinear equation is associated with the AKNS spectral problem. In the nonlocal case, the squared eigenfunction of the <span>(L)</span> operator leads to some changes in the term of the source that affect the motion of solitons. The soliton solutions of the nonlocal nonlinear Schrödinger equation with self-consistent sources are presented using the inverse scattering transform. The dynamics of the solitons are illustrated, which differ from those of the nonlocal equation without a source. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"219 3","pages":"933 - 943"},"PeriodicalIF":1.0,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503134","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Translation-invariant Gibbs measures for the Ising–Potts model on a second-order Cayley tree 二阶 Cayley 树上 Ising-Potts 模型的平移不变吉布斯量纲
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-06-25 DOI: 10.1134/S0040577924060114
M. M. Rakhmatullaev, B. M. Isakov
{"title":"Translation-invariant Gibbs measures for the Ising–Potts model on a second-order Cayley tree","authors":"M. M. Rakhmatullaev,&nbsp;B. M. Isakov","doi":"10.1134/S0040577924060114","DOIUrl":"10.1134/S0040577924060114","url":null,"abstract":"<p> We consider a mixed-type model given by the three-state Ising–Potts model on a Cayley tree. A criterion for the existence of limit Gibbs measures for this model on an arbitrary-order Cayley tree is obtained. Translation-invariant Gibbs measures on a second-order Cayley tree are studied. The existence of a phase transition is proved: a range of parameter values is found in which there are one to seven Gibbs measures for the three-state Ising–Potts model. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"219 3","pages":"1048 - 1059"},"PeriodicalIF":1.0,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141514127","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Cosymmetries of chiral-type systems 手性型系统的对称性
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-06-25 DOI: 10.1134/S0040577924060084
A. V. Balandin
{"title":"Cosymmetries of chiral-type systems","authors":"A. V. Balandin","doi":"10.1134/S0040577924060084","DOIUrl":"10.1134/S0040577924060084","url":null,"abstract":"<p> We consider chiral-type systems admitting a Lax representation with values in a real or complex semisimple Lie algebra such that an additional regularity condition is satisfied (one of the matrices is a regular element of the Lie algebra). We prove that for a chiral-type system with vanishing torsion and a nonvanishing curvature, the existence of at least one pointwise cosymmetry is a necessary condition for the regular Lax representation. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"219 3","pages":"992 - 1003"},"PeriodicalIF":1.0,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141514124","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Revisiting solutions of the Adler–Bobenko–Suris lattice equations and lattice Boussinesq-type equations 重新审视阿德勒-博本科-苏里斯晶格方程和晶格布辛斯方程的解法
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-06-25 DOI: 10.1134/S0040577924060059
Song-lin Zhao, Ke Yan, Ying-ying Sun
{"title":"Revisiting solutions of the Adler–Bobenko–Suris lattice equations and lattice Boussinesq-type equations","authors":"Song-lin Zhao,&nbsp;Ke Yan,&nbsp;Ying-ying Sun","doi":"10.1134/S0040577924060059","DOIUrl":"10.1134/S0040577924060059","url":null,"abstract":"<p> Solutions of all Adler–Bobenko–Suris equations except <span>(Q4)</span>, and of several lattice Boussinesq-type equations are reconsidered by using the Cauchy matrix approach. By introducing a “fake” nonautonomous plane-wave factor, we derive soliton solutions, oscillatory solutions, and semi-oscillatory solutions of the target lattice equations. Unlike the conventional soliton solutions, the oscillatory solutions take constant values on all elementary quadrilaterals on <span>(mathbb{Z}^2)</span>, which demonstrates a periodic structure. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"219 3","pages":"944 - 972"},"PeriodicalIF":1.0,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141514121","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Expansion of hypergeometric functions in terms of polylogarithms with a nontrivial change of variables 超几何函数的多对数展开与非微妙的变量变化
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-06-25 DOI: 10.1134/S0040577924060011
M. A. Bezuglov, A. I. Onishchenko
{"title":"Expansion of hypergeometric functions in terms of polylogarithms with a nontrivial change of variables","authors":"M. A. Bezuglov,&nbsp;A. I. Onishchenko","doi":"10.1134/S0040577924060011","DOIUrl":"10.1134/S0040577924060011","url":null,"abstract":"<p> Hypergeometric functions of one and many variables play an important role in various branches of modern physics and mathematics. We often encounter hypergeometric functions with indices linearly dependent on a small parameter with respect to which we need to perform Laurent expansions. Moreover, it is desirable that such expansions be expressed in terms of well-known functions that can be evaluated with arbitrary precision. To solve this problem, we use the method of differential equations and the reduction of corresponding differential systems to a canonical basis. In this paper, we are interested in the generalized hypergeometric functions of one variable and in the Appell and Lauricella functions and their expansions in terms of the Goncharov polylogarithms. Particular attention is paid to the case of rational indices of the considered hypergeometric functions when the reduction to the canonical basis involves a nontrivial variable change. The paper comes with a Mathematica package <span>Diogenes</span>, which provides an algorithmic implementation of the required steps. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"219 3","pages":"871 - 896"},"PeriodicalIF":1.0,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503131","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Multibreather-like solutions of the real and complex reverse space–time nonlocal defocusing short-pulse equations 实数和复数反向时空非局部散焦短脉冲方程的多散焦样解
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-06-25 DOI: 10.1134/S0040577924060060
Hui Mao
{"title":"Multibreather-like solutions of the real and complex reverse space–time nonlocal defocusing short-pulse equations","authors":"Hui Mao","doi":"10.1134/S0040577924060060","DOIUrl":"10.1134/S0040577924060060","url":null,"abstract":"<p> Multibreather-like solutions in determinant form for the real and complex reverse space–time nonlocal defocusing short-pulse equations are constructed via Darboux transformations and nonlocal reductions. It is shown that the multibreather-like solutions of these two equations can be obtained only by reducing the even multisoliton solutions of the two-component short-pulse equation. As examples, <span>(1,2)</span>-breather-like solutions and their dynamics are illustrated graphically. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"219 3","pages":"973 - 985"},"PeriodicalIF":1.0,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141514122","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Gauge equivalence of (1+1) Calogero–Moser–Sutherland field theory and a higher-rank trigonometric Landau–Lifshitz model 1+1$$卡洛吉罗-莫瑟-萨瑟兰场论与高阶三角兰道-利夫希茨模型的等价性
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-06-25 DOI: 10.1134/S0040577924060096
K. R. Atalikov, A. V. Zotov
{"title":"Gauge equivalence of (1+1) Calogero–Moser–Sutherland field theory and a higher-rank trigonometric Landau–Lifshitz model","authors":"K. R. Atalikov,&nbsp;A. V. Zotov","doi":"10.1134/S0040577924060096","DOIUrl":"10.1134/S0040577924060096","url":null,"abstract":"<p> We consider the classical integrable <span>((1+1))</span> trigonometric <span>(gl_N)</span> Landau–Lifshitz models constructed by means of quantum <span>(R)</span>-matrices that also satisfy the associative Yang–Baxter equation. It is shown that a <span>((1+1))</span> field analogue of the trigonometric Calogero–Moser–Sutherland model is gauge equivalent to the Landau–Lifshitz model that arises from the Antonov–Hasegawa–Zabrodin trigonometric nonstandard <span>(R)</span>-matrix. The latter generalizes Cherednik’s <span>(7)</span>-vertex <span>(R)</span>-matrix in the <span>(GL_2)</span> case to the case of <span>(GL_N)</span>. An explicit change of variables between the <span>((1+1))</span> models is obtained. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"219 3","pages":"1004 - 1017"},"PeriodicalIF":1.0,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141514125","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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