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Lie group geometry: Riemann and Ricci tensors and normal forms of Lie algebras 李群几何：黎曼和利玛窦张量及列代数的正常形式
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-11-26 DOI: 10.1134/S0040577924110011
A. V. Borovskikh
{"title":"Lie group geometry: Riemann and Ricci tensors and normal forms of Lie algebras","authors":"A. V. Borovskikh","doi":"10.1134/S0040577924110011","DOIUrl":"10.1134/S0040577924110011","url":null,"abstract":"<p> In the context of the connection discovered in a preceding paper between left-invariant objects (both geometric and dynamical) defined on a Lie group and the algebra of right automorphisms (the dual algebra), we consider the representation of the main geometric characteristics via this algebra and the corresponding metric form. These characteristics are shown to be constant (independent of a point) and defined only by the structure constants of the dual algebra and the coefficients of the metric form. Due to this connection, it is possible to introduce the concept of normal forms of a Lie algebra. Reducing any algebra and any metric to normal form in fact consists in reducing two quadratic forms to canonical form: first, the metric is reduced to the sum of squares of linear differential forms, and then the constant matrix characterizing the Ricci tensor is reduced to diagonal form (with the principal curvatures appearing on the diagonal). It turns out that there are only two different normal forms for three-dimensional Lie algebras, each depending on three parameters associated with three principal curvatures in the general case. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"221 2","pages":"1777 - 1798"},"PeriodicalIF":1.0,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714480","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
On the unique solvability of the div–curl problem in unbounded domains and energy estimates of solutions 关于无界域中 div-curl 问题的唯一可解性和解的能量估计
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-11-26 DOI: 10.1134/S0040577924110023
A. V. Gorshkov
{"title":"On the unique solvability of the div–curl problem in unbounded domains and energy estimates of solutions","authors":"A. V. Gorshkov","doi":"10.1134/S0040577924110023","DOIUrl":"10.1134/S0040577924110023","url":null,"abstract":"<p> We study the problem of reconstructing a solenoidal vector field from a vortex function with a no-slip condition on the boundary of an external two-dimensional domain. A solvability criterion is obtained as a condition for the orthogonality of the vortex function to harmonic functions. We also obtain some estimates of the solution in the spaces <span>(L_2)</span> and <span>(H_1)</span>. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"221 2","pages":"1799 - 1812"},"PeriodicalIF":1.0,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714481","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
Nonlocal abstract Ginzburg–Landau-type equations and applications 非局部抽象金兹堡-朗道型方程及其应用
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-11-26 DOI: 10.1134/S0040577924110060
V. B. Shakhmurov
{"title":"Nonlocal abstract Ginzburg–Landau-type equations and applications","authors":"V. B. Shakhmurov","doi":"10.1134/S0040577924110060","DOIUrl":"10.1134/S0040577924110060","url":null,"abstract":"<p> We study a nonlocal abstract Ginzburg–Landau type equation. The equation includes variable coefficients with convolution terms and an abstract linear operator function <span>(A)</span> in a Fourier-type Banach space <span>(E)</span>. For sufficiently smooth initial data, assuming growth conditions for the operator <span>(A)</span> and the coefficient <span>(a)</span>, the existence and uniqueness of the solution and the <span>(L^p)</span> -regularity properties are established. We obtain the existence and uniqueness of the solution, and the regularity of different classes of nonlocal Ginzburg–Landau-type equations by choosing the space <span>(E)</span> and operator <span>(A)</span> that occur in a wide variety of physical systems. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"221 2","pages":"1867 - 1881"},"PeriodicalIF":1.0,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714488","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
Binary Bargmann symmetry constraint and algebro-geometric solutions of a semidiscrete integrable hierarchy 半离散可积分层次结构的二元巴格曼对称性约束和积分几何解
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-11-26 DOI: 10.1134/S0040577924110084
Yaxin Guan, Xinyue Li, Qiulan Zhao
{"title":"Binary Bargmann symmetry constraint and algebro-geometric solutions of a semidiscrete integrable hierarchy","authors":"Yaxin Guan,&nbsp;Xinyue Li,&nbsp;Qiulan Zhao","doi":"10.1134/S0040577924110084","DOIUrl":"10.1134/S0040577924110084","url":null,"abstract":"<p> We present the binary Bargmann symmetry constraint and algebro-geometric solutions for a semidiscrete integrable hierarchy with a bi-Hamiltonian structure. First, we derive a hierarchy associated with a discrete spectral problem by applying the zero-curvature equation and study its bi-Hamiltonian structure. Then, resorting to the binary Bargmann symmetry constraint for the potentials and eigenfunctions, we decompose the hierarchy into an integrable symplectic map and finite-dimensional integrable Hamiltonian systems. Moreover, with the help of the characteristic polynomial of the Lax matrix, we propose a trigonal curve encompassing two infinite points. On this trigonal curve, we introduce a stationary Baker–Akhiezer function and a meromorphic function, and analyze their asymptotic properties and divisors. Based on these preparations, we obtain algebro-geometric solutions for the hierarchy in terms of the Riemann theta function. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"221 2","pages":"1901 - 1928"},"PeriodicalIF":1.0,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714486","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
Total, classical, and quantum uncertainty matrices via operator monotone functions 通过算子单调函数计算总不确定性矩阵、经典不确定性矩阵和量子不确定性矩阵
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-11-26 DOI: 10.1134/S0040577924110035
Yajing Fan, Nan Li, Shunlong Luo
{"title":"Total, classical, and quantum uncertainty matrices via operator monotone functions","authors":"Yajing Fan,&nbsp;Nan Li,&nbsp;Shunlong Luo","doi":"10.1134/S0040577924110035","DOIUrl":"10.1134/S0040577924110035","url":null,"abstract":"<p> It is important to distinguish between classical information and quantum information in quantum information theory. In this paper, we first extend the concept of metric-adjusted correlation measure and some related measures to non-Hermitian operators, and establish several relations between the metric-adjusted skew information with different operator monotone functions. By employing operator monotone functions, we next introduce three uncertainty matrices generated by channels: the total uncertainty matrix, the classical uncertainty matrix, and the quantum uncertainty matrix. We establish a decomposition of the total uncertainty matrix into classical and quantum parts and further investigate their basic properties. As applications, we employ uncertainty matrices to quantify the decoherence caused by the action of quantum channels on quantum states, and calculate the uncertainty matrices of some typical channels to reveal certain intrinsic features of the corresponding channels. Moreover, we establish several uncertainty relations that improve the traditional Heisenberg uncertainty relations involving variance. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"221 2","pages":"1813 - 1835"},"PeriodicalIF":1.0,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714482","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
Form factors of local operators in the generalized algebraic Bethe ansatz 广义代数贝特方差中局部算子的形式因子
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-11-26 DOI: 10.1134/S0040577924110102
G. Kulkarni, N. A. Slavnov
{"title":"Form factors of local operators in the generalized algebraic Bethe ansatz","authors":"G. Kulkarni,&nbsp;N. A. Slavnov","doi":"10.1134/S0040577924110102","DOIUrl":"10.1134/S0040577924110102","url":null,"abstract":"<p> We consider an <span>(XYZ)</span> spin chain within the framework of the generalized algebraic Bethe ansatz. We study form factors of local operators corresponding to singlet states in the free-fermion limit. We obtain explicit representations for these form factors. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"221 2","pages":"1940 - 1958"},"PeriodicalIF":1.0,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714489","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
3D consistency of negative flows 负流量的三维一致性
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-11-26 DOI: 10.1134/S0040577924110047
V. E. Adler
{"title":"3D consistency of negative flows","authors":"V. E. Adler","doi":"10.1134/S0040577924110047","DOIUrl":"10.1134/S0040577924110047","url":null,"abstract":"<p> We study the <span>(3)</span>D-consistency property for negative symmetries of KdV-type equations. Its connection with the <span>(3)</span>D consistency of discrete equations is explained. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"221 2","pages":"1836 - 1851"},"PeriodicalIF":1.0,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714483","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
Dynamical description of the phase transition to the superconducting state 超导状态相变的动力学描述
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-11-26 DOI: 10.1134/S0040577924110126
L. A. Gosteva, M. Yu. Nalimov, A. S. Yashugin
{"title":"Dynamical description of the phase transition to the superconducting state","authors":"L. A. Gosteva,&nbsp;M. Yu. Nalimov,&nbsp;A. S. Yashugin","doi":"10.1134/S0040577924110126","DOIUrl":"10.1134/S0040577924110126","url":null,"abstract":"<p> We present dynamical equations that are valid in the vicinity of a phase transition to the superconducting state. In writing the equations, we take the possible influence of the magnetic interaction between charge carriers and temperature fluctuations into account. We discuss the type of the phase transition under study. We argue in favor of the applicability of stochastic dynamical model A according to the standard classification (the stochastic model with one two-component field without a conservation law) to describe the dynamics of this phase transition. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"221 2","pages":"1981 - 1993"},"PeriodicalIF":1.0,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714491","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
On noncommutative modified KP systems 关于非交换修正 KP 系统
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-11-26 DOI: 10.1134/S0040577924110072
Zheng Wang, Chuanzhong Li
{"title":"On noncommutative modified KP systems","authors":"Zheng Wang,&nbsp;Chuanzhong Li","doi":"10.1134/S0040577924110072","DOIUrl":"10.1134/S0040577924110072","url":null,"abstract":"<p> We investigate the gauge transformations of the noncommutative modified KP hierarchy and the noncommutative constrained modified KP hierarchy in the Kupershmidt–Kiso version. By introducing the Orlov–Schulman operator, which depends on time variables and dressing operators, we construct the quantum torus symmetry for the noncommutative modified KP hierarchy. We also give a recursion operator for the noncommutative constrained modified KP hierarchy. We present an extended noncommutative modified KP hierarchy. The compatibility equations between the noncommutative modified KP flows and the extended noncommutative modified KP flows are constructed. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"221 2","pages":"1882 - 1900"},"PeriodicalIF":1.0,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714485","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
Cauchy matrix approach to novel extended semidiscrete KP-type systems 新型扩展半离散 KP 型系统的考奇矩阵方法
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-11-26 DOI: 10.1134/S0040577924110096
Hong-juan Tian, A. Silem
{"title":"Cauchy matrix approach to novel extended semidiscrete KP-type systems","authors":"Hong-juan Tian,&nbsp;A. Silem","doi":"10.1134/S0040577924110096","DOIUrl":"10.1134/S0040577924110096","url":null,"abstract":"<p> Two novel extended semidiscrete KP-type systems, namely, partial differential–difference systems with one continuous and two discrete variables, are investigated. Introducing an arbitrary function into the Cauchy matrix function or the plane wave factor allows implementing extended integrable systems within the Cauchy matrix approach. We introduce the bilinear <span>(DDelta^2)</span>KP system, the extended <span>(DDelta^2)</span>pKP, <span>(DDelta^2)</span>pmKP, and <span>(DDelta^2)</span>SKP systems, all of which are based on the Cauchy matrix approach. This results in a diversity of solutions for these extended systems as contrasted to the usual multiple soliton solutions. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"221 2","pages":"1929 - 1939"},"PeriodicalIF":1.0,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714487","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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