Theoretical and Mathematical Physics最新文献

{"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":null,"pages":null},"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}

{"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":null,"pages":null},"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}

{"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":null,"pages":null},"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}

{"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":null,"pages":null},"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}

{"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":null,"pages":null},"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}

{"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":null,"pages":null},"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}

{"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":null,"pages":null},"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}

{"title":"Monopoles, spectra of overlap fermions, and eta-prime meson in external magnetic fields","authors":"M. Hasegawa","doi":"10.1134/S0040577924060102","DOIUrl":"10.1134/S0040577924060102","url":null,"abstract":"<p> The effects of external magnetic fields on monopoles, spectra of the overlap Dirac operator, instantons, and the mass of the eta-prime meson are examined by conducting lattice QCD simulations. The uniform external magnetic field is applied to gauge field configurations with <span>(N_f=2+1)</span> flavor quarks. The bare quark masses are tuned in order to obtain the physical values of the pion mass and of the <span>(m_s/m_{u,d})</span> ratio. Standard configurations and configurations with an applied external magnetic field are generated in the color confinement and deconfinement phases. The intensity of the external magnetic field varies from <span>(e|B|=0.57,mathrm{GeV}^2)</span> to <span>(e|B|=1.14,mathrm{GeV}^2)</span>. To examine the influence of the external magnetic field on monopoles, we first calculate the monopole density, measure the lengths of the monopole loops, and compare them with the absolute value of the Polyakov loops. Next, using the generated configurations, we compute the eigenvalues and eigenvectors of the overlap Dirac operator, which preserves exact chiral symmetry. To investigate how external magnetic fields affect the spectra of the overlap Dirac operator, we compute spectral densities, compare fluctuations of the eigenvalues of the overlap Dirac operator with the predictions of random matrix theory, and estimate the number of instantons and anti-instantons from the topological charges. In addition, we analyze smearing effects on these observables and chiral symmetry breaking. Finally, we calculate the decay constant of the pseudoscalar meson, the chiral condensate, and the square mass of the eta-prime meson using the eigenvalues and eigenvectors. We then extrapolate the numerical results in the chiral limit and demonstrate the effects of external magnetic fields on the extrapolation results. This article presents preliminary results. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141514126","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}

{"title":"Generalized theta series and monodromy of a Casimir connection. Case of rank 1","authors":"E. I. Dotsenko","doi":"10.1134/S0040577924050015","DOIUrl":"10.1134/S0040577924050015","url":null,"abstract":"<p> The monodromy of the <span>(mathfrak{sl}(2))</span> Casimir connection is considered. It is shown that the trace of the monodromy operator over an appropriate space of flat sections gives the Jacobi theta constant and incomplete theta functions. A definition of new objects, namely, incomplete Appell–Lerch sums, is given, and their connection with the trace of the monodromy operator is revealed. </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":"141149341","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}

{"title":"Fractional multiple trapping model of time-of-flight transient photocurrents in amorphous semiconductors","authors":"Y. Goutal,&nbsp;F. Serdouk,&nbsp;A. Boumali,&nbsp;M. L. Benkhedir","doi":"10.1134/S0040577924050118","DOIUrl":"10.1134/S0040577924050118","url":null,"abstract":"<p> The use of the multiple-trapping (MT) model to comprehend the transport of nonequilibrium charge carriers in amorphous semiconductors has proven highly effective. Under specific conditions, this model generates anomalous diffusion equations characterized by fractional time derivatives. This underscores the utility of the MT model in interpreting fractional transport equations, establishing initial and boundary conditions, and developing numerical methods for solving fractional kinetic equations. Also, this work provides a concise overview of applying fractional MT equations to address challenges in time-of-flight (TOF) experiments. Furthermore, it delves into the connection between the MT model and generalized fractional kinetic equations. In addition, the study introduces analytic approximate solutions of the fractional diffusion equation, incorporating MT phenomena and employing Laplace transforms. This approach is suitable for analyzing both the pre- and post-regimes of TOF transient current, applicable to amorphous semiconductors that display either nondispersive or dispersive transport characteristics. The effectiveness of this method is illustrated through numerical simulations of TOF transient current using the inverse Laplace transform technique with the Padé approximation. The practicality of the method is confronted with the experimental data obtained from thin films of amorphous selenium (a-Se), and the results of this confrontation are deemed satisfactory. The results of this study offer a new promising perspective for the two following reasons. First, employing fractional calculus to address the MT equations introduces a distinct approach compared to methodologies in the existing literature. This is substantiated by the inclusion of memory effects in fractional calculus, implying that the present solution is influenced by preceding time steps. Second, the numerical results demonstrate good agreement with experimental data. Consequently, the introduction of fractional calculus has the potential to offer fresh insights into the behavior of charge carriers in amorphous semiconductors. </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":"141151887","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}