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Asymptotics of hypergeometric coherent states and eigenfunctions of the hydrogen atom in a magnetic field. Determination of self-consistent energy levels 氢原子在磁场中的超几何相干态和本征函数的渐近性。自洽能级的测定
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-03-25 DOI: 10.1134/S0040577925030067
A. V. Pereskokov
{"title":"Asymptotics of hypergeometric coherent states and eigenfunctions of the hydrogen atom in a magnetic field. Determination of self-consistent energy levels","authors":"A. V. Pereskokov","doi":"10.1134/S0040577925030067","DOIUrl":"10.1134/S0040577925030067","url":null,"abstract":"<p> The spectral problem for the hydrogen atom in a magnetic field perturbed by a self-consistent field is considered. An asymptotic expansion of self-consistent energy levels is obtained. An asymptotic expansion of hypergeometric coherent states near the sphere <span>(|q|=2)</span> is found. The asymptotics of the norm of the asymptotic eigenfunctions in the space <span>(L^2(mathbb{R}^3))</span> is calculated. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"222 3","pages":"453 - 470"},"PeriodicalIF":1.0,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143688526","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
Influence of the electrodynamic stability of streaming fluid cylinders surrounded by dielectric gravitational fluid under a radial-varying electric field 径向变电场作用下介电重力流体包围流液缸电动力稳定性的影响
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-03-25 DOI: 10.1134/S0040577925030079
M. H. Hendy
{"title":"Influence of the electrodynamic stability of streaming fluid cylinders surrounded by dielectric gravitational fluid under a radial-varying electric field","authors":"M. H. Hendy","doi":"10.1134/S0040577925030079","DOIUrl":"10.1134/S0040577925030079","url":null,"abstract":"<p> We study the relation between the electrodynamic stabilization of self-gravitating dielectric fluid cylinders with varying densities subjected to radially varying electric fields. We derive the perturbations for all models studied. The electric fields inside and outside the fluid cylinder stabilize the system across different densities and wavelengths. Additionally, the use of a magnetic field is identified as a potentially effective method to inhibit the onset of unstable motion. Gravitational marginal stability occurs when the two densities are equal. Stable and unstable regions are determined for two densities at each wavelength in all symmetric and nonsymmetric axial perturbations. The effect of streaming is significant and destabilizing: it reduces the stable regions and enlarges the capillary axisymmetric unstable domain. Furthermore, we identify the necessary conditions to contain gravitational instability. The results are interpreted physically and analytically, and are confirmed numerically. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"222 3","pages":"471 - 482"},"PeriodicalIF":1.0,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143688528","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
First triplet four-electron state in the impurity Hubbard model. Three-dimensional case 杂质哈伯德模型中的第一三重态四电子态。三维情况下
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-03-25 DOI: 10.1134/S0040577925030092
R. T. Parmanova
{"title":"First triplet four-electron state in the impurity Hubbard model. Three-dimensional case","authors":"R. T. Parmanova","doi":"10.1134/S0040577925030092","DOIUrl":"10.1134/S0040577925030092","url":null,"abstract":"<p> We consider the energy operator of a four-electron system in the impurity Hubbard model and investigate the structure of essential spectra and the discrete spectrum of the system in the first triplet state on the three-dimensional lattice. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"222 3","pages":"497 - 510"},"PeriodicalIF":1.0,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143688529","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
Loop, cuspon, and soliton solutions of a multicomponent discrete complex short-pulse equation 多分量离散复杂短脉冲方程的环解、逆解和孤子解
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-02-25 DOI: 10.1134/S0040577925020047
A. Inam, M. ul Hassan
{"title":"Loop, cuspon, and soliton solutions of a multicomponent discrete complex short-pulse equation","authors":"A. Inam,&nbsp;M. ul Hassan","doi":"10.1134/S0040577925020047","DOIUrl":"10.1134/S0040577925020047","url":null,"abstract":"<p> We present an integrable discretization of a multicomponent discrete complex short-pulse (dCSP) equation in terms of a Lax pair representation and a Darboux transformation (DT). The Lax pair representation is explored using block matrices by extending the <span>(2times2)</span> Lax matrices to <span>(2^Ltimes2^L)</span> Lax matrices. The DT on the matrix solutions is studied and is used to generate solutions of the multicomponent dCSP equation by using the properties of quasideterminants. By expanding the quasideterminants, we then show the soliton solutions to be expressed as ratios of ordinary determinants. Further, an appropriate continuum limit is applied to obtain multisoliton solutions of the continuous complex short-pulse equation. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"222 2","pages":"228 - 251"},"PeriodicalIF":1.0,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143489410","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
Evolution of plane perturbations in the cosmological environment of the Higgs scalar field and an ideal scalar-charged fluid 在希格斯标量场和理想标量带电流体的宇宙学环境中平面扰动的演化
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-02-25 DOI: 10.1134/S0040577925020072
Yu. G. Ignat’ev
{"title":"Evolution of plane perturbations in the cosmological environment of the Higgs scalar field and an ideal scalar-charged fluid","authors":"Yu. G. Ignat’ev","doi":"10.1134/S0040577925020072","DOIUrl":"10.1134/S0040577925020072","url":null,"abstract":"<p> A model of an ideal fluid with a scalar charge is formulated, on the basis of which a model with a neutral fluid and a vacuum-field model with transition rules between them are constructed. We qualitatively analyze the obtained dynamical systems and model them numerically. A mathematical model of plane longitudinal scalar–gravitational perturbations of the Friedmann ideal charged fluid with Higgs interaction is formulated. It is shown that gravitational perturbations do not arise in the absence of the fluid, i.e., in the vacuum-field model. Perturbations of the scalar field are possible only in those cases where the cosmological system is at singular points in the unperturbed state. In these cases, exact solutions of the field equation are found in terms of Bessel functions of the first and second kind; they describe damped oscillations in the case of a stable unperturbed state and growing oscillations in the case of an unstable unperturbed state. The WKB theory of plane scalar–gravitational perturbations is constructed: dispersion equations are obtained in the general form and are solved for a neutral fluid. Expressions are obtained for the local frequency and growth increment of oscillations, as well as the integral increment. It is shown that only free wave regimes or growing standing oscillations are possible during the evolution. Perturbations in the WKB approximation in a neutral fluid are studied and it is shown that local formulas for the evolution of perturbations correspond to the 1985 model of Khlopov, Malomed, and Zeldovich. The times of the beginning and end of the instability phase are determined and it is shown that instability can develop only at the unstable inflationary stage of the expansion of the Universe. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"222 2","pages":"285 - 313"},"PeriodicalIF":1.0,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143489579","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
Black brane/Bose gas duality and the third law of thermodynamics 黑球/玻色气体二元性与热力学第三定律
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-02-25 DOI: 10.1134/S0040577925020060
I. Ya. Aref’eva, I. V. Volovich, D. O. Stepanenko
{"title":"Black brane/Bose gas duality and the third law of thermodynamics","authors":"I. Ya. Aref’eva,&nbsp;I. V. Volovich,&nbsp;D. O. Stepanenko","doi":"10.1134/S0040577925020060","DOIUrl":"10.1134/S0040577925020060","url":null,"abstract":"<p> In the thermodynamics of black holes in an asymptotically flat space, the third law of thermodynamics is violated, and entropy cannot be consistently modeled through conventional statistical mechanics. Notably, the third law of thermodynamics is violated for the Schwarzschild black hole, and its entropy can only be described using an unconventional model, such as the Bose gas in negative dimensions. In contrast, for certain black brane solutions, such as the Poincaré AdS black branes, Lifshitz black branes, and anisotropic Lifshitz-type black branes, the third law is preserved, with entropy vanishing as the temperature approaches zero. In this paper, we extend the previously established duality between black hole and Bose gas thermodynamics to black branes. Specifically, the Poincaré black brane in <span>(D)</span> spacetime dimensions corresponds to a nonrelativistic Bose gas in <span>(2(D-2))</span> spatial dimensions. Furthermore, the duality between Lifshitz branes and Bose gases relates a Lifshitz brane with the exponent <span>(alpha)</span> in <span>(D)</span>-dimensional spacetime to a Bose gas of quasiparticles with the energy <span>(k^alpha)</span> in <span>(D-2)</span> spatial dimensions. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"222 2","pages":"276 - 284"},"PeriodicalIF":1.0,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143489578","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 solvability of the Cauchy problem for a thermal–electrical model 热电模型Cauchy问题的可解性
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-02-25 DOI: 10.1134/S0040577925020011
M. V. Artemeva, M. O. Korpusov, A. A. Panin
{"title":"On the solvability of the Cauchy problem for a thermal–electrical model","authors":"M. V. Artemeva,&nbsp;M. O. Korpusov,&nbsp;A. A. Panin","doi":"10.1134/S0040577925020011","DOIUrl":"10.1134/S0040577925020011","url":null,"abstract":"<p> We consider a thermal–electrical <span>((3+1))</span>-dimensional model of semiconductor heating in an electric field. We prove the existence of a classical solution nonextendable in time for the corresponding Cauchy problem. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"222 2","pages":"183 - 197"},"PeriodicalIF":1.0,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143489409","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
A (bar{partial})-method for the ((2+1))-dimensional coupled Boussinesq equation and its integrable extension ((2+1))维耦合Boussinesq方程的(bar{partial}) -方法及其可积扩展
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-02-25 DOI: 10.1134/S0040577925020035
Huanhuan Lu, Xinan Ren
{"title":"A (bar{partial})-method for the ((2+1))-dimensional coupled Boussinesq equation and its integrable extension","authors":"Huanhuan Lu,&nbsp;Xinan Ren","doi":"10.1134/S0040577925020035","DOIUrl":"10.1134/S0040577925020035","url":null,"abstract":"<p> The content of this paper is divided into two parts. Starting from the Lax pair with a spectral function <span>(psi(x,y,t,k))</span>, the <span>(bar{partial})</span>-dressing method is used to investigate the <span>((2+1))</span>-dimensional coupled Boussinesq equation, thereby constructing the scattering equation in the form of a linear <span>(bar{partial})</span> problem, and ultimately deriving the reconstruction formula for the solutions. By complexifying each independent variable of the <span>((2+1))</span>-dimensional coupled Boussinesq equation, we construct its generalizations to <span>((4+2))</span> dimensions. The spectral analysis of the <span>(t)</span>-independent part of the Lax pair with a spectral function <span>(chi(x,y,t,k))</span> together with the nonlocal <span>(bar{partial})</span> formalism yield the representation for the solution of the <span>(bar{partial})</span> problem. Additionally, the nonlinear Fourier transform pair comprising both direct and inverse transforms is successfully worked out. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"222 2","pages":"211 - 227"},"PeriodicalIF":1.0,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143489372","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
Duffin–Kemmer–Petiau oscillator in topologically charged Ellis–Bronnikov-type wormhole 拓扑带电ellis - bronnikov型虫洞中的Duffin-Kemmer-Petiau振子
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-02-25 DOI: 10.1134/S0040577925020084
H. Aounallah, A. Moussa, F. Ahmed, P. Rudra
{"title":"Duffin–Kemmer–Petiau oscillator in topologically charged Ellis–Bronnikov-type wormhole","authors":"H. Aounallah,&nbsp;A. Moussa,&nbsp;F. Ahmed,&nbsp;P. Rudra","doi":"10.1134/S0040577925020084","DOIUrl":"10.1134/S0040577925020084","url":null,"abstract":"<p> We explore relativistic quantum dynamics of spin-<span>(0)</span> bosonic fields governed by the Duffin–Kemmer–Petiau (DKP) equation within the context of a topologically charged Ellis–Bronnikov-type wormhole. We derive the radial equation for the quantum systems described by the DKP equation on this wormhole background, ultimately arriving at the confluent Heun differential equation form. As a specific case, we present the ground energy level and the corresponding wave function of this quantum system. Furthermore, we extend our investigation to the DKP oscillator in the considered wormhole background, employing a similar methodology to deduce the ground state energy levels and wave function of the quantum oscillator field. Additionally, we introduce a zeroth component of the electromagnetic four-vector potential and examine the DKP oscillator by considering two types of potential on this wormhole background. Our findings highlight the influence of the wormhole throat radius and the topological charge of the geometry. Moreover, we observe that different external potentials also impact the energy levels of this relativistic quantum system. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"222 2","pages":"314 - 331"},"PeriodicalIF":1.0,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143489635","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
Solutions of three nonlocal equations with self-consistent sources by the inverse scattering transform and reductions 用逆散射变换和约简解具有自洽源的三个非局部方程
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-02-25 DOI: 10.1134/S0040577925020023
Qi Li, Hai-Qing Huang, Qiu-Yuan Duan
{"title":"Solutions of three nonlocal equations with self-consistent sources by the inverse scattering transform and reductions","authors":"Qi Li,&nbsp;Hai-Qing Huang,&nbsp;Qiu-Yuan Duan","doi":"10.1134/S0040577925020023","DOIUrl":"10.1134/S0040577925020023","url":null,"abstract":"<p> Based on the Lax pairs and inverse scattering theory, we propose a reduction method by which we naturally reduce the AKNS hierarchy with self-consistent sources to several nonlocal nonlinear integrable hierarchies with self-consistent sources. The key is the properties of the squared eigenfunctions and scattering data associated with the AKNS scattering problems under symmetry conditions, and reducing the number of sources by half. By the reductions, we derive three nonlocal hierarchies including the nonlocal nonlinear Schrödinger hierarchy with self-consistent sources, the nonlocal complex modified Korteweg–de Vries hierarchy with self-consistent sources, and the nonlocal modified Korteweg–de Vries hierarchy with self-consistent sources, as well as their soliton solutions. As an example, we describe the shape and motion of a one-soliton solution of the nonlocal modified Korteweg–de Vries equation with self-consistent sources and compare it with its counterpart without sources. This reduction method can be applied to both nonlocal and classical (local) reductions of the AKNS hierarchy with self-consistent sources. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"222 2","pages":"198 - 210"},"PeriodicalIF":1.0,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143489411","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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