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Gibbs measures for fertile models with hard-core interactions and four states 具有硬核相互作用和四种状态的肥沃模型的吉布斯测量法
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-05-24 DOI: 10.1134/S0040577924050106
R. M. Khakimov, B. Z. Tojiboev
{"title":"Gibbs measures for fertile models with hard-core interactions and four states","authors":"R. M. Khakimov,&nbsp;B. Z. Tojiboev","doi":"10.1134/S0040577924050106","DOIUrl":"10.1134/S0040577924050106","url":null,"abstract":"<p> We consider fertile models with hard interactions, four states, and an activity parameter <span>(lambda&gt;0)</span> on a Cayley tree. We show that there are three types of such models: “stick,” “key,” and “generalized key.” For the “generalized key” model on a Cayley tree of order <span>(k=4)</span>, the uniqueness of the translation-invariant Gibbs measure is proved, and conditions for the existence of double-periodic Gibbs measures other than the translation-invariant ones are found. Moreover, in the case of a fertile graph of the “stick” type, the translation invariance of double-periodic Gibbs measures on a Cayley tree of orders <span>(k=2,3,4)</span> is shown and conditions for the existence of double-periodic Gibbs measures other than the translation-invariant ones on a Cayley tree of order <span>(kgeq5)</span> are found. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141137063","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
Spinors corresponding to modified orthogonal frames in Euclidean 3-space 欧氏三维空间中修正正交框架对应的旋光子
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-05-24 DOI: 10.1134/S0040577924050027
A. Z. Azak, T. Erişir
{"title":"Spinors corresponding to modified orthogonal frames in Euclidean 3-space","authors":"A. Z. Azak,&nbsp;T. Erişir","doi":"10.1134/S0040577924050027","DOIUrl":"10.1134/S0040577924050027","url":null,"abstract":"<p> The space of spinors, defined as the basic representation of a Clifford algebra, can be expressed as the spin representation of an orthogonal Lie algebra. At the same time, these spin representations can also be characterized as finite-dimensional projective representations of the special orthogonal group. From a geometrical perspective, the behavior of spinors under the action of Lie groups can be examined. Thus, one has the advantage of making a concrete and basic explanation about what spinors are in a geometrical sense. In this study, the spinor representations of an orthogonal frame moving on a analytic curve is investigated geometrically. The spinor equations corresponding to a modified orthogonal frame and a modified orthogonal frame with <span>(tau)</span> are derived. The relations between modified orthogonal frames and the Frenet frame are established regarding their spinor formulations. Our motivation in this paper is to give spinor representations of the modified orthogonal frame. Consequently, this study has been planned as an interdisciplinary study between Clifford algebras and geometry. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141132509","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 photon emission by a variable electromagnetic field 关于可变电磁场的光子发射
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-05-24 DOI: 10.1134/S004057792405009X
V. V. Skobelev
{"title":"On the photon emission by a variable electromagnetic field","authors":"V. V. Skobelev","doi":"10.1134/S004057792405009X","DOIUrl":"10.1134/S004057792405009X","url":null,"abstract":"<p> We generalize and supplement the results of the original paper written with the participation of the author half a century ago; in that paper, the nonlinear effect of the photon emission by a variable electromagnetic field was first described. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141144702","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 blow-up of the solution of a ((1+1))-dimensional thermal–electrical model 关于$$(1+1)$$维热-电模型解的膨胀问题
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-05-24 DOI: 10.1134/S0040577924050040
M. V. Artemeva, M. O. Korpusov
{"title":"On the blow-up of the solution of a ((1+1))-dimensional thermal–electrical model","authors":"M. V. Artemeva,&nbsp;M. O. Korpusov","doi":"10.1134/S0040577924050040","DOIUrl":"10.1134/S0040577924050040","url":null,"abstract":"<p> We consider a <span>((1+1))</span>-dimensional thermal–electrical model of semiconductor heating in an electric field. For the corresponding initial-boundary value problem, we prove the existence of a classical solution that cannot be continued in time and obtain sufficient conditions for the blow-up of the solution in a finite time. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141134700","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
Self-gravitating Higgs field of scalar charge 标量电荷的自引力希格斯场
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-05-24 DOI: 10.1134/S0040577924050088
Yu. G. Ignat’ev
{"title":"Self-gravitating Higgs field of scalar charge","authors":"Yu. G. Ignat’ev","doi":"10.1134/S0040577924050088","DOIUrl":"10.1134/S0040577924050088","url":null,"abstract":"<p> We study the self-gravitating Higgs field of a scalar charge. We show that in the zeroth and first approximation in the smallness of the scalar charge, the gravitational field of the scalar charge is described by the Schwarzschild–de Sitter metric with a cosmological constant determined by the vacuum potential of the Higgs field. An equation for the perturbation of the vacuum potential is obtained and studied. Particular exact solutions of the field equation are given. It is shown that in the case of a naked singularity, solutions of the field equation have the character of microscopic oscillations with a Compton wavelength. Asymptotic limit cases of the behavior of solutions are studied and their comparative analysis is carried out in relation to the Fisher solution. The averaging of microscopic oscillations of the scalar field is carried out and it it shown that at <span>(Lambda&gt;0)</span> they make a negative contribution to the macroscopic energy of the scalar field, reducing the observed value of the black hole mass. A computer simulation of a scalar field demonstrates various types of the behavior of solutions. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141149337","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
Particle creation in cosmological space–time by a time-varying electric field 时变电场在宇宙时空中创造粒子
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-05-24 DOI: 10.1134/S004057792405012X
H. Rezki, S. Zaim
{"title":"Particle creation in cosmological space–time by a time-varying electric field","authors":"H. Rezki,&nbsp;S. Zaim","doi":"10.1134/S004057792405012X","DOIUrl":"10.1134/S004057792405012X","url":null,"abstract":"<p> We use the semiclassical approach to solve the Klein–Gordon and Dirac equations in the presence of a time-varying electric field. Our objective is to calculate the density of particle creation in a cosmological anisotropic Bianchi- I space–time. We demonstrate that when the electric interaction is proportional to the Ricci scalar of curved space–time, the distribution of particles subjected to the electric field transforms into a thermal state. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141152009","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
Soliton solutions of the negative-order nonlinear Schrödinger equation 负阶非线性薛定谔方程的孤子解
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-05-24 DOI: 10.1134/S0040577924050052
G. U. Urazboev, I. I. Baltaeva, A. K. Babadjanova
{"title":"Soliton solutions of the negative-order nonlinear Schrödinger equation","authors":"G. U. Urazboev,&nbsp;I. I. Baltaeva,&nbsp;A. K. Babadjanova","doi":"10.1134/S0040577924050052","DOIUrl":"10.1134/S0040577924050052","url":null,"abstract":"<p> We discuss the integration of the Cauchy problem for the negative-order nonlinear Schrödinger equation in the class of rapidly decreasing functions via the inverse scattering problem method. In particular, we obtain the time dependence of scattering data of the Zakharov–Shabat system with the potential that is a solution of the considered problem. We give an explicit representation of the one-soliton solution of the negative-order nonlinear Schrödinger equation based on the obtained results. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141142326","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
Generation of higher-dimensional isospectral–nonisospectral integrable hierarchies associated with a new class of higher-dimensional column-vector loop algebras 生成与一类新的高维列向量环代数相关的高维等谱-非等谱可积分层次结构
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-05-24 DOI: 10.1134/S0040577924050039
Haifeng Wang, Yufeng Zhang
{"title":"Generation of higher-dimensional isospectral–nonisospectral integrable hierarchies associated with a new class of higher-dimensional column-vector loop algebras","authors":"Haifeng Wang,&nbsp;Yufeng Zhang","doi":"10.1134/S0040577924050039","DOIUrl":"10.1134/S0040577924050039","url":null,"abstract":"<p> We construct a new class of higher-dimensional column-vector loop algebras. Based on it, a method for generating higher-dimensional isospectral–nonisospectral integrable hierarchies is proposed. As an application, we derive a generalized nonisospectral integrable Schrödinger hierarchy that can be reduced to the famous derivative nonlinear Schrödinger equation. By using the higher-dimensional column-vector loop algebras, we obtain an extended isospectral–nonisospectral integrable Schrödinger hierarchy that can be reduced to many classical and new equations, such as the extended nonisospectral derivative nonlinear Schrödinger system, the heat equation, and the Fokker–Planck equation, which has a wide range of applications in stochastic dynamical systems. Furthermore, we deduce a <span>(Z_N^varepsilon)</span> nonisospectral integrable Schrödinger hierarchy, which means that the coupling results are extended to an arbitrary number of components. Additionally, the Hamiltonian structures of these hierarchies are discussed by using the quadratic form trace identity. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141149295","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 constrained (q)-mKP hierarchy: Additional symmetry and a hidden Virasoro algebraic structure 关于受约束的 $$q$$-mKP 层次结构：附加对称性和隐藏的维拉索罗代数结构
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-05-24 DOI: 10.1134/S0040577924050076
Song Li, Kelei Tian, Ying Xu, Ge Yi
{"title":"On the constrained (q)-mKP hierarchy: Additional symmetry and a hidden Virasoro algebraic structure","authors":"Song Li,&nbsp;Kelei Tian,&nbsp;Ying Xu,&nbsp;Ge Yi","doi":"10.1134/S0040577924050076","DOIUrl":"10.1134/S0040577924050076","url":null,"abstract":"<p> We construct the additional symmetry of the constrained <span>(q)</span>-mKP hierarchy. The new modified operator is introduced. The flows and additional flows acting on the modified operator are given. The additional flows acting on the eigenfunction and the adjoint eigenfunction are presented. The hidden Virasoro algebraic structure in the additional symmetry of the constrained <span>(q)</span>-mKP hierarchy is given. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141138234","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
Parity–time symmetric solitons of the complex KP equation 复 KP 方程的奇偶时对称孤子
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-05-24 DOI: 10.1134/S0040577924050064
Jen-Hsu Chang
{"title":"Parity–time symmetric solitons of the complex KP equation","authors":"Jen-Hsu Chang","doi":"10.1134/S0040577924050064","DOIUrl":"10.1134/S0040577924050064","url":null,"abstract":"<p> We construct the parity–time symmetric solitons of the complex KP equation using the totally nonnegative Grassmannian. We obtain that every element in the totally nonnegative orthogonal Grassmannian corresponds to a parity–time symmetric soliton solution. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141149342","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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