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Dimensional reduction of nonlinear differential equations on homogeneous spaces 齐次空间上非线性微分方程的降维
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-05-26 DOI: 10.1134/S0040577925050046
O. L. Kurnyavko, I. V. Shirokov
{"title":"Dimensional reduction of nonlinear differential equations on homogeneous spaces","authors":"O. L. Kurnyavko,&nbsp;I. V. Shirokov","doi":"10.1134/S0040577925050046","DOIUrl":"10.1134/S0040577925050046","url":null,"abstract":"<p> We consider the problem of dimensional reduction of nonlinear differential equations on homogeneous spaces that have no symmetries in general. The proposed method allows passing to a differential equation with fewer independent variables and, in particular, to ordinary differential equations. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"223 2","pages":"755 - 769"},"PeriodicalIF":1.0,"publicationDate":"2025-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144140257","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
Néel temperature of a quasi-two-dimensional triangular-lattice antiferromagnet 准二维三角形晶格反铁磁体的纳米温度
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-05-26 DOI: 10.1134/S0040577925050083
V. V. Val’kov, A. S. Martynov, D. M. Dzebisashvili
{"title":"Néel temperature of a quasi-two-dimensional triangular-lattice antiferromagnet","authors":"V. V. Val’kov,&nbsp;A. S. Martynov,&nbsp;D. M. Dzebisashvili","doi":"10.1134/S0040577925050083","DOIUrl":"10.1134/S0040577925050083","url":null,"abstract":"<p> Based on the atomic representation for spin operators in the case of an arbitrary value of the spin <span>(S)</span>, we study the influence of quantum fluctuations on spin-wave renormalizations of the Néel temperature <span>(T_mathrm{N})</span> and on the magnetization of quasi-two-dimensional triangular-lattice antiferromagnet sublattices. The application of combined Green’s functions constructed using spin operators and their partial components allows easily obtaining a closed system of equations determining not only all branches of the spectrum of collective excitations but also the occupation numbers of states of an atom with different values of the spin projection. We show that the renormalization of <span>(T_mathrm{N})</span> is expressed in terms of the generalized Watson integral. Its nontrivial dependence on the degree of quasi-two-dimensionality and on the dynamical properties of three spectral branches determines the behavior of the critical temperature in the cases of different relations between the parameters of the quasi-two-dimensional antiferromagnet. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"223 2","pages":"826 - 838"},"PeriodicalIF":1.0,"publicationDate":"2025-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144140252","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
Integrable Hamiltonians related to the (mathfrak{e}(3)), (mathfrak{so}(4)), and (mathfrak{so}(3,1)) Poisson brackets 与(mathfrak{e}(3))(mathfrak{so}(4))和(mathfrak{so}(3,1))泊松括号相关的可积哈密顿量
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-05-26 DOI: 10.1134/S0040577925050034
V. V. Sokolov
{"title":"Integrable Hamiltonians related to the (mathfrak{e}(3)), (mathfrak{so}(4)), and (mathfrak{so}(3,1)) Poisson brackets","authors":"V. V. Sokolov","doi":"10.1134/S0040577925050034","DOIUrl":"10.1134/S0040577925050034","url":null,"abstract":"<p> We present a brief overview of our results on new integrable cases in Hamiltonian mechanics. The paper is devoted to a description of quadratic Hamiltonians that have an additional integral of motion in the cases of linear Poisson brackets <span>(mathfrak{e}(3))</span>, <span>(mathfrak{so}(4))</span> and <span>(mathfrak{so}(3,1))</span>. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"223 2","pages":"742 - 754"},"PeriodicalIF":1.0,"publicationDate":"2025-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144140256","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 (k)th higher Nash blow-up derivation Lie algebras of isolated hypersurface singularities 关于(k)孤立超曲面奇点的高Nash爆破导数李代数
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-05-26 DOI: 10.1134/S0040577925050022
N. Hussain, S. S.-T. Yau, Huaiqing Zuo
{"title":"On the (k)th higher Nash blow-up derivation Lie algebras of isolated hypersurface singularities","authors":"N. Hussain,&nbsp;S. S.-T. Yau,&nbsp;Huaiqing Zuo","doi":"10.1134/S0040577925050022","DOIUrl":"10.1134/S0040577925050022","url":null,"abstract":"<p> Many physical questions such as <span>(4d)</span> <span>(N=2)</span> superconformal field theories, the Coulomb branch spectrum, and the Seiberg–Witten solutions are related to singularities. In this paper, we introduce some new invariants <span>(mathcal L^k_n(V))</span>, <span>(rho_n^k)</span>, and <span>(d_n^k(V))</span> of isolated hypersurface singularities <span>((V,0))</span>. We give a new conjecture for the characterization of simple curve singularities using the <span>(k)</span>th higher Nash blow-up derivation Lie algebra <span>(mathcal L^k_n(V))</span>. This conjecture is verified for small <span>(n)</span> and <span>(k)</span>. A inequality conjecture for <span>(rho_n^k)</span> and <span>(d_n^k(V))</span> is proposed. These two conjectures are verified for binomial singularities. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"223 2","pages":"705 - 741"},"PeriodicalIF":1.0,"publicationDate":"2025-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144140200","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
Pseudosolution of an integral convolution equation of the first kind 第一类积分卷积方程的伪解
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-05-26 DOI: 10.1134/S0040577925050113
N. B. Yengibaryan
{"title":"Pseudosolution of an integral convolution equation of the first kind","authors":"N. B. Yengibaryan","doi":"10.1134/S0040577925050113","DOIUrl":"10.1134/S0040577925050113","url":null,"abstract":"<p> We consider the equation <span>(int_{0}^{r}T(|x-t|)f(t),dt =g(x))</span>, where <span>(r&lt;infty)</span> and the functions <span>(T)</span> and <span>(g)</span> and their first derivatives are absolutely continuous on <span>([0,r])</span> and <span>(T'(0)ne 0)</span>. An arbitrary term <span>(ax+b)</span> is added to the right-hand side of the equation. The obtained family of equations is reduced by double differentiation to an equation of the second kind. In the case of its unique solvability in <span>(L_{1}(0,r))</span>, the solution <span>(tilde{f})</span> is called a <span>(D^{2})</span>-pseudosolution of the original equation. We introduce the partial regularization of the equation and present some cases of the existence of a <span>(D^{2})</span>-pseudosolution. We propose a criterion for the suitability of <span>(tilde{f})</span> as an approximate solution. The problem of constructing a pseudosolution of an equation on the half-line is discussed. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"223 2","pages":"872 - 877"},"PeriodicalIF":1.0,"publicationDate":"2025-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144140255","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
Debye mass in the accelerating frame 加速坐标系中的德拜质量
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-05-26 DOI: 10.1134/S0040577925050095
D. V. Diakonov, K. V. Bazarov
{"title":"Debye mass in the accelerating frame","authors":"D. V. Diakonov,&nbsp;K. V. Bazarov","doi":"10.1134/S0040577925050095","DOIUrl":"10.1134/S0040577925050095","url":null,"abstract":"<p> We consider a conformal scalar field theory with the <span>(lambda phi^4)</span> self-coupling in Rindler and Minkowski coordinates at a finite-temperature with the Planckian distribution for exact modes. The solution of the one-loop Dyson–Schwinger equation is found through the order <span>(lambda^{3/2})</span>. The appearance of a thermal (Debye) mass is shown. Unlike the physical mass, the thermal mass gives a gap in the energy spectrum in the quantization in the Rindler coordinates. The difference between such calculations in Minkowski and Rindler coordinates for exact modes is discussed. It is also shown that states with a temperature lower than the Unruh temperature are unstable. It is proved that for the canonical Unruh temperature, the thermal mass is equal to zero. The contribution to the quantum average of the stress–energy tensor is also calculated, it remains traceless even in the presence of the thermal mass. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"223 2","pages":"839 - 862"},"PeriodicalIF":1.0,"publicationDate":"2025-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144140201","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
Quantifying measurement incompatibility via measurement disturbance 通过测量干扰量化测量不相容
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-05-26 DOI: 10.1134/S0040577925050071
Yi Guo, Shunlong Luo
{"title":"Quantifying measurement incompatibility via measurement disturbance","authors":"Yi Guo,&nbsp;Shunlong Luo","doi":"10.1134/S0040577925050071","DOIUrl":"10.1134/S0040577925050071","url":null,"abstract":"<p> The incompatibility between quantum measurements (as mathematically represented by positive operator-valued measures, i.e., POVMs) is a key feature of quantum mechanics and is intrinsically related to the noncommutativity of operators. For both theoretical and practical considerations, it is desirable to quantify the degree of incompatibility between quantum measurements, and considerable effort has been devoted to this issue. In this paper, we provide a novel approach to measurement incompatibility by exploiting the Lüders channels derived from POVMs and employing the measurement disturbance to quantify incompatibility. This is achieved by constructing an approximately joint measurement for a pair of POVMs, which is an enlarged POVM with the correct marginal property for one of the two POVMs but not necessarily for the other. The degree of failure of the marginal property for the other POVM is a kind of measurement disturbance and can be naturally interpreted as a quantifier of the incompatibility between the two POVMs. We reveal basic properties of this quantifier of measurement incompatibility, identify its maximal value in some cases, compare it with several popular measures in the literature, and illustrate it with some typical examples. Some related open issues are also discussed. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"223 2","pages":"810 - 825"},"PeriodicalIF":1.0,"publicationDate":"2025-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144140251","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
Universality of stochastic Laplacian growth 随机拉普拉斯增长的通用性
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-05-26 DOI: 10.1134/S0040577925050010
O. V. Alekseev
{"title":"Universality of stochastic Laplacian growth","authors":"O. V. Alekseev","doi":"10.1134/S0040577925050010","DOIUrl":"10.1134/S0040577925050010","url":null,"abstract":"<p> We consider a stochastic Laplacian growth model within the framework of normal random matrices. In the limit of large matrix size, the support of eigenvalues forms a planar domain with a sharp boundary that evolves stochastically as the matrix size increases. We show that the most probable growth scenario is similar to deterministic Laplacian growth, while alternative scenarios illustrate the impact of fluctuations. We prove that the probability distribution function of fluctuations is given by the circular unitary ensemble introduced by Dyson in 1962. The partition function of fluctuations is shown to be universal, depending solely on the fluctuation intensity and the problem’s geometry, regardless of the initial domain shape. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"223 2","pages":"691 - 704"},"PeriodicalIF":1.0,"publicationDate":"2025-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144140253","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
Rational solutions of nonautonomous quadrilateral equations by the bilinearization of Bäcklund transformation systems Bäcklund变换系统双线性化非自治四边形方程的有理解
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-04-25 DOI: 10.1134/S0040577925040051
Danda Zhang, Liya Zhu, Yingying Sun
{"title":"Rational solutions of nonautonomous quadrilateral equations by the bilinearization of Bäcklund transformation systems","authors":"Danda Zhang,&nbsp;Liya Zhu,&nbsp;Yingying Sun","doi":"10.1134/S0040577925040051","DOIUrl":"10.1134/S0040577925040051","url":null,"abstract":"<p> Rational solutions of several nonautonomous quadrilateral equations in the ABS and ABS* list are obtained in a neat form of Casoratians, which mostly relies on a single <span>(tau)</span> function. The corresponding nonautonomous bilinear equations are listed in difference and differential–difference forms by introducing an auxiliary variable. Instead of bilinearizing quadrilateral equations, we present their related Bäcklund transformation systems, which directly reduce to bilinear equations by specific transformations. As an application, a result related to the discrete Painlevé equation is given. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"223 1","pages":"576 - 596"},"PeriodicalIF":1.0,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143875267","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
Integration of the generalized Camassa–Holm equation in the class of periodic functions 周期函数类中广义Camassa-Holm方程的积分
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-04-25 DOI: 10.1134/S0040577925040075
B. A. Babajanov, D. O. Atajonov
{"title":"Integration of the generalized Camassa–Holm equation in the class of periodic functions","authors":"B. A. Babajanov,&nbsp;D. O. Atajonov","doi":"10.1134/S0040577925040075","DOIUrl":"10.1134/S0040577925040075","url":null,"abstract":"<p> We study periodic solutions of the generalized Camassa–Holm equation (CH-<span>(gamma)</span> equation). We show that the generalized CH-<span>(gamma)</span> equation is also an important theoretical model because it is a completely integrable system. We obtain representation for periodic solutions of the generalized CH-<span>(gamma)</span> equation in the framework of the inverse spectral problem for a weighted Sturm–Liouville operator. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"223 1","pages":"624 - 635"},"PeriodicalIF":1.0,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143875424","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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