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Boundedness-below conditions for a general scalar potential of two real scalar fields and the Higgs boson 两个实标量场和希格斯玻色子的一般标量势的有界-无界条件
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-09-24 DOI: 10.1134/S0040577924090101
Yisheng Song, Liqun Qi
{"title":"Boundedness-below conditions for a general scalar potential of two real scalar fields and the Higgs boson","authors":"Yisheng Song,&nbsp;Liqun Qi","doi":"10.1134/S0040577924090101","DOIUrl":"10.1134/S0040577924090101","url":null,"abstract":"<p> The most general scalar potential of two real scalar fields and a Higgs boson is a quartic homogeneous polynomial in three variables, which defines a <span>(4)</span>th-order three-dimensional symmetric tensor. Hence, the boundedness of such a scalar potential from below involves the positive (semi-)definiteness of the corresponding tensor. In this paper, we therefore mainly discuss analytic expressions of positive (semi-)definiteness for such a special tensor. First, an analytically necessary and sufficient condition is given to test the positive (semi-)definiteness of a <span>(4)</span>th-order two-dimensional symmetric tensor. Furthermore, by means of such a result, the analytic necessary and sufficient conditions of the boundedness from below are obtained for a general scalar potential of two real scalar fields and the Higgs boson. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"220 3","pages":"1567 - 1579"},"PeriodicalIF":1.0,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142413504","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 positive fixed points of operator of Hammerstein type with degenerate kernel and Gibbs measures 论具有退化核的哈默斯坦型算子的正定点和吉布斯量纲
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-09-24 DOI: 10.1134/S0040577924090113
I. M. Mavlonov, Kh. N. Khushvaktov, G. P. Arzikulov, F. H. Haydarov
{"title":"On positive fixed points of operator of Hammerstein type with degenerate kernel and Gibbs measures","authors":"I. M. Mavlonov,&nbsp;Kh. N. Khushvaktov,&nbsp;G. P. Arzikulov,&nbsp;F. H. Haydarov","doi":"10.1134/S0040577924090113","DOIUrl":"10.1134/S0040577924090113","url":null,"abstract":"<p> It is known that translation-invariant Gibbs measures of a model with an uncountable set of spin values can be described by positive fixed points of a nonlinear integral operator of Hammerstein type. Significant results have been obtained on positive fixed points of a Hammerstein-type operator with a degenerate kernel, but the existence of Gibbs measures corresponding to the fixed points have not been proved for constructed kernels. We construct new degenerate kernels of the Hammerstein operator in the context of the theory of Gibbs measures, and show that each positive fixed point of the operator gives a translation-invariant Gibbs measure. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"220 3","pages":"1580 - 1588"},"PeriodicalIF":1.0,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142413443","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
Exact solution of the problem of the interaction between a point charge and an insulator with nonlinear susceptibility 点电荷与具有非线性易感性的绝缘体之间相互作用问题的精确解答
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-09-24 DOI: 10.1134/S0040577924090095
A. A. Belov, M. A. Tintul, P. A. Polyakov
{"title":"Exact solution of the problem of the interaction between a point charge and an insulator with nonlinear susceptibility","authors":"A. A. Belov,&nbsp;M. A. Tintul,&nbsp;P. A. Polyakov","doi":"10.1134/S0040577924090095","DOIUrl":"10.1134/S0040577924090095","url":null,"abstract":"<p> We construct a new exact solution of the problem of a filament placed parallel to the interface between two insulators, one of which has a nonlinear susceptibility. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"220 3","pages":"1556 - 1566"},"PeriodicalIF":1.0,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142413611","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
Explicit multiple solitons of the mixed Chen–Lee–Liu equation derived from the Riemann–Hilbert approach 从黎曼-希尔伯特方法导出陈-李-刘混合方程的显式多重孤子
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-09-24 DOI: 10.1134/S0040577924090071
Yumin Zheng, Yunqing Yang, Yongshuai Zhang, Wei Liu
{"title":"Explicit multiple solitons of the mixed Chen–Lee–Liu equation derived from the Riemann–Hilbert approach","authors":"Yumin Zheng,&nbsp;Yunqing Yang,&nbsp;Yongshuai Zhang,&nbsp;Wei Liu","doi":"10.1134/S0040577924090071","DOIUrl":"10.1134/S0040577924090071","url":null,"abstract":"<p> The Riemann–Hilbert approach is applied to the mixed Chen–Lee–Liu equation. The corresponding Jost solutions are found, the analytic, asymptotic and symmetric properties of Jost solutions are studied, and a modified Riemann–Hilbert problem is constructed that satisfies the normalization condition. The formulas for multiple solitons related to the simple poles of the Riemann–Hilbert problem are given in determinant form. According to the Cauchy–Binet formula, the formulas for multiple solitons are given explicitly. Based on these explicit formulas, the first- and second-order solitons are obtained, and the multiple-soliton collisions are verified to be elastic. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"220 3","pages":"1515 - 1529"},"PeriodicalIF":1.0,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142413610","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
Method for estimating the number of zeros of the spatially one-dimensional Pauli–Jordan–Dirac function on spatial intervals using the Kronecker theorem 利用克罗内克定理估算空间区间上空间一维保利-乔丹-狄拉克函数零点个数的方法
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-09-24 DOI: 10.1134/S0040577924090022
E. A. Karatsuba
{"title":"Method for estimating the number of zeros of the spatially one-dimensional Pauli–Jordan–Dirac function on spatial intervals using the Kronecker theorem","authors":"E. A. Karatsuba","doi":"10.1134/S0040577924090022","DOIUrl":"10.1134/S0040577924090022","url":null,"abstract":"<p> We investigate the properties of the Pauli–Jordan–Dirac anticommutator of the quantum field theory of free Dirac electrons in a discrete representation in the spatially one-dimensional case and present a method for estimating the number of zeros of the anticommutator on spatial intervals using the Kronecker theorem. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"220 3","pages":"1429 - 1439"},"PeriodicalIF":1.0,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142413487","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
Nonlinear dynamics of a two-axis ferromagnet on the semiaxis 半轴上双轴铁磁体的非线性动力学
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-09-24 DOI: 10.1134/S0040577924090034
V. V. Kiselev
{"title":"Nonlinear dynamics of a two-axis ferromagnet on the semiaxis","authors":"V. V. Kiselev","doi":"10.1134/S0040577924090034","DOIUrl":"10.1134/S0040577924090034","url":null,"abstract":"<p> Using the spectral transform on a torus, we solve the initial–boundary value problem for quasi-one-dimensional excitations in a semibounded ferromagnet, taking the exchange interaction, orthorhombic anisotropy, and magnetostatic fields into account. We used the mixed boundary conditions whose limit cases correspond to free and fully pinned spins at the sample edge. We predict and analyze new types of solitons (moving domain walls and precessing breathers), whose cores are strongly deformed near the sample boundary. At large distances from the sample surface, they take the form of typical solitons in an unbounded medium. We analyze the properties of the reflection of solitons from the sample boundary depending on the degree of spin pinning at the surface. We obtain new conservation laws that guarantee the true boundary conditions to hold when solitons reflect from the sample surface. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"220 3","pages":"1440 - 1470"},"PeriodicalIF":1.0,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142413614","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 properties of a diffusion-coupled system of differential equations with an additional internal coupling 具有额外内部耦合的扩散耦合微分方程系统的动态特性
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-08-26 DOI: 10.1134/S0040577924080038
L. I. Ivanovskiy
{"title":"Dynamical properties of a diffusion-coupled system of differential equations with an additional internal coupling","authors":"L. I. Ivanovskiy","doi":"10.1134/S0040577924080038","DOIUrl":"10.1134/S0040577924080038","url":null,"abstract":"<p> We study the dynamics of a system of differential equations with the diffusion interaction and an additional internal coupling. Such systems are interesting because a slight variation in the coefficient at the additional coupling allows obtaining intricate scenarios of phase rearrangements. For the system under study, we find the critical dependence of the parameters such that zero equilibrium loses stability as two spatially inhomogeneous states appear in one case and a cycle in another case. With the parameter values close to the critical ones, asymptotic formulas are obtained for the regimes that branch off from the zero solution. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"220 2","pages":"1282 - 1293"},"PeriodicalIF":1.0,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177150","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
Generalized Chaos game in an extended hyperbolic plane 扩展双曲面中的广义混沌博弈
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-08-26 DOI: 10.1134/S0040577924080099
L. N. Romakina, I. V. Ushakov
{"title":"Generalized Chaos game in an extended hyperbolic plane","authors":"L. N. Romakina,&nbsp;I. V. Ushakov","doi":"10.1134/S0040577924080099","DOIUrl":"10.1134/S0040577924080099","url":null,"abstract":"<p> We propose and theoretically substantiate an algorithm for conducting a generalized Chaos game with an arbitrary jump on finite convex polygons of the extended hyperbolic plane <span>(H^2)</span> whose components in the Cayley–Klein projective model are the Lobachevsky plane and its ideal domain. In particular, the defining identities for a point dividing an elliptic, hyperbolic, or parabolic segment in a given ratio are proved, and formulas for calculating the coordinates of such a point at a canonical frame of the first type are obtained. The results of a generalized Chaos game conducted using the advanced software package pyv are presented. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"220 2","pages":"1361 - 1384"},"PeriodicalIF":1.0,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177156","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
Stationary thermal front in the problem of reconstructing the semiconductor thermal conductivity coefficient using simulation data 利用模拟数据重建半导体导热系数问题中的静态热前沿
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-08-26 DOI: 10.1134/S0040577924080026
M. A. Davydova, G. D. Rublev
{"title":"Stationary thermal front in the problem of reconstructing the semiconductor thermal conductivity coefficient using simulation data","authors":"M. A. Davydova,&nbsp;G. D. Rublev","doi":"10.1134/S0040577924080026","DOIUrl":"10.1134/S0040577924080026","url":null,"abstract":"<p> We study the problem of the existence of stationary, asymptotically Lyapunov-stable solutions with internal transition layers in nonlinear heat conductance problems with a thermal flow containing a negative exponent. We formulate sufficient conditions for the existence of classical solutions with internal layers in such problems. We construct an asymptotic approximation of an arbitrary-order for the solution with a transition layer. We substantiate the algorithm for constructing the formal asymptotics and study the asymptotic Lyapunov stability of the stationary solution with an internal layer as a solution of the corresponding parabolic problem with the description of the local attraction domain of the stable stationary solution. As an application, we present a new effective method for reconstructing the nonlinear thermal conductivity coefficient with a negative exponent using the position of the stationary thermal front in combination with observation data. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"220 2","pages":"1262 - 1281"},"PeriodicalIF":1.0,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142223486","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
Kramers–Wannier duality and Tutte polynomials 克拉默-万尼尔对偶性和图特多项式
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-08-26 DOI: 10.1134/S0040577924080051
A. A. Kazakov
{"title":"Kramers–Wannier duality and Tutte polynomials","authors":"A. A. Kazakov","doi":"10.1134/S0040577924080051","DOIUrl":"10.1134/S0040577924080051","url":null,"abstract":"<p> We study applications of the connection between the partition functions of the Potts models and Tutte polynomials: it is demonstrated how the Kramers–Wannier duality can be derived from the Tutte duality. Using the “contraction–elimination” relation and the Biggs formalism, we derive the high-temperature expansion and discuss possible methods for generalizing the Kramers–Wannier duality to models on nonplanar graphs. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"220 2","pages":"1304 - 1314"},"PeriodicalIF":1.0,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142223487","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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