Theoretical and Mathematical Physics最新文献

{"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":"219 3","pages":"1018 - 1047"},"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":"219 2","pages":"705 - 711"},"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":"219 2","pages":"839 - 855"},"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}

{"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":"219 2","pages":"823 - 838"},"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}

{"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":"219 2","pages":"712 - 721"},"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}

{"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":"219 2","pages":"806 - 822"},"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}

{"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":"219 2","pages":"748 - 760"},"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}

{"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":"219 2","pages":"792 - 805"},"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}

{"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":"219 2","pages":"856 - 870"},"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}

{"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":"219 2","pages":"761 - 769"},"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}