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Dynamics of a Klein–Gordon oscillator in the presence of a cosmic string in the Som–Raychaudhuri space–time Som-Raychaudhuri时空中存在宇宙弦时克莱因-戈登振子的动力学
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-12-25 DOI: 10.1134/S0040577924120134
A. Bouzenada, A. Boumali, R. L. L. Vitória, C. Furtado
{"title":"Dynamics of a Klein–Gordon oscillator in the presence of a cosmic string in the Som–Raychaudhuri space–time","authors":"A. Bouzenada,&nbsp;A. Boumali,&nbsp;R. L. L. Vitória,&nbsp;C. Furtado","doi":"10.1134/S0040577924120134","DOIUrl":"10.1134/S0040577924120134","url":null,"abstract":"<p> We explore the dynamics of the Klein–Gordon oscillator in the presence of a cosmic string in the Som–Raychaudhuri space–time. The exact solutions for the free and oscillator cases are obtained and discussed. These solutions reveal the effects of the cosmic string and space–time geometry on bosonic particles. To illustrate these results, several figures and tables are included. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"221 3","pages":"2193 - 2206"},"PeriodicalIF":1.0,"publicationDate":"2024-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889871","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
Lie algebraic approach to the Hellmann Hamiltonian by considering perturbation method 考虑微扰方法的海尔曼哈密顿量的李代数逼近
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-12-25 DOI: 10.1134/S0040577924120092
H. Rahmati
{"title":"Lie algebraic approach to the Hellmann Hamiltonian by considering perturbation method","authors":"H. Rahmati","doi":"10.1134/S0040577924120092","DOIUrl":"10.1134/S0040577924120092","url":null,"abstract":"<p> We show that the Lie algebraic approach with the perturbation method can be used to study the eigenvalues of the Hellmann Hamiltonian. The key element is the Runge–Lenz vector, which appears in problems with radial symmetry. This symmetry implies that the proper lie algebra for these Hamiltonians is <span>(so(4))</span>, which is a sum of two <span>(so(3))</span> Lie algebras and requires symmetry of the angular momentum vector <span>(vec{L})</span> and the Runge–Lenz vector <span>(vec{M})</span>, and therefore their cross products as <span>(vec{W}=vec{L}timesvec{M})</span>. Here, Yukawa potential is considered as a perturbation term, which is added to the Coulomb Hamiltonian to produce the Hellmann Hamiltonian. Lie algebraically, the perturbation term adds a magnitude of precession rate <span>(Omega)</span> to all three operators <span>(vec{L})</span>, <span>(vec{M})</span>, and <span>(vec{W})</span>. Topologically, we show that the appearance of this precession has a significant effect on the spectrum and the corresponding Lie algebra of the Hellmann potential. By using Lie algebraic properties of the Runge–Lenz vector and using the Kolmogorov method, we obtain the energy spectrum of this Hamiltonian. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"221 3","pages":"2144 - 2154"},"PeriodicalIF":1.0,"publicationDate":"2024-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142890487","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
Inverse scattering transform for the focusing Hirota equation with asymmetric boundary conditions 非对称边界条件下聚焦Hirota方程的逆散射变换
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-12-25 DOI: 10.1134/S0040577924120079
Chunjiang Wang, Jian Zhang
{"title":"Inverse scattering transform for the focusing Hirota equation with asymmetric boundary conditions","authors":"Chunjiang Wang,&nbsp;Jian Zhang","doi":"10.1134/S0040577924120079","DOIUrl":"10.1134/S0040577924120079","url":null,"abstract":"<p> We formulate an inverse scattering transformation for the focusing Hirota equation with asymmetric boundary conditions, which means that the limit values of the solution at spatial infinities have different amplitudes. For the direct problem, we do not use Riemann surfaces, but instead analyze the branching properties of the scattering problem eigenvalues. The Jost eigenfunctions and scattering coefficients are defined as single-valued functions on the complex plane, and their analyticity properties, symmetries, and asymptotics are obtained, which are helpful in constructing the corresponding Riemann–Hilbert problem. On an open contour, the inverse problem is described by a Riemann–Hilbert problem with double poles. Finally, for comparison purposes, we consider the initial value problem with one-sided nonzero boundary conditions and obtain the formulation of the inverse scattering transform by using Riemann surfaces. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"221 3","pages":"2109 - 2131"},"PeriodicalIF":1.0,"publicationDate":"2024-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889882","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
Equation with a lower negative time number in the Davey–Stewartson hierarchy 在Davey-Stewartson层次结构中具有较低负时间数的方程
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-12-25 DOI: 10.1134/S004057792412002X
A. K. Pogrebkov
{"title":"Equation with a lower negative time number in the Davey–Stewartson hierarchy","authors":"A. K. Pogrebkov","doi":"10.1134/S004057792412002X","DOIUrl":"10.1134/S004057792412002X","url":null,"abstract":"<p> Earlier, we have presented an integrable system with a negative time variable number for the Davey–Stewartson hierarchy. Here, we develop this approach to construct an integrable equation with a lower time variable number. In addition, we show that the system reduced with respect to this time yields a new integrable equation in <span>(1+1)</span> dimensions. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"221 3","pages":"2022 - 2030"},"PeriodicalIF":1.0,"publicationDate":"2024-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889915","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 multicomponent generalized nonisospectral super AKNS integrable hierarchy 多分量广义非等谱超AKNS可积层次
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-12-25 DOI: 10.1134/S0040577924120067
Jinxiu Li, Haifeng Wang
{"title":"A multicomponent generalized nonisospectral super AKNS integrable hierarchy","authors":"Jinxiu Li,&nbsp;Haifeng Wang","doi":"10.1134/S0040577924120067","DOIUrl":"10.1134/S0040577924120067","url":null,"abstract":"<p> In the nonisospectral case, we introduce the associated spectral problem with a perturbation term. We obtain a generalized nonisospectral super AKNS hierarchy and a coupled generalized nonisospectral super AKNS hierarchy associated with generalized Lie superalgebras <span>(sl(2,1))</span> and <span>(sl(4,1))</span>. Based on a new type of multicomponent Lie superalgebra <span>(sl(2N,1))</span>, a multicomponent generalized nonisospectral super AKNS hierarchy is obtained. By using the supertrace identity, the super bi-Hamiltonian structures of the resulting superintegrable hierarchies are obtained. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"221 3","pages":"2083 - 2108"},"PeriodicalIF":1.0,"publicationDate":"2024-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889880","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 existence of a nonextendable solution of the Cauchy problem for a ((3+1))-dimensional thermal–electrical model 关于((3+1))维热电模型Cauchy问题不可扩展解的存在性
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-12-25 DOI: 10.1134/S0040577924120146
M. V. Artemeva, M. O. Korpusov
{"title":"On the existence of a nonextendable solution of the Cauchy problem for a ((3+1))-dimensional thermal–electrical model","authors":"M. V. Artemeva,&nbsp;M. O. Korpusov","doi":"10.1134/S0040577924120146","DOIUrl":"10.1134/S0040577924120146","url":null,"abstract":"<p> A thermal–electrical <span>((3+1))</span>-dimensional model of heating a semiconductor in an electric field is considered. For the corresponding Cauchy problem, the existence of a classical solution nonextendable in time is proved and an a priori estimate global in time is obtained. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"221 3","pages":"2207 - 2218"},"PeriodicalIF":1.0,"publicationDate":"2024-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142890537","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 spectrum of the Landau Hamiltonian perturbed by a periodic smooth electric potential 在朗道哈密顿谱上被周期性平滑电势扰动
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-12-25 DOI: 10.1134/S0040577924120110
L. I. Danilov
{"title":"On the spectrum of the Landau Hamiltonian perturbed by a periodic smooth electric potential","authors":"L. I. Danilov","doi":"10.1134/S0040577924120110","DOIUrl":"10.1134/S0040577924120110","url":null,"abstract":"<p> We study the spectrum of the Landau Hamiltonian with a periodic electric potential. In the case of a rational magnetic flux, we present examples of nonconstant zero-mean periodic electric potentials <span>({Vin C^{infty}(mathbb{R}^2;mathbb{R})})</span> for which the spectrum has an eigenvalue at the second Landau level. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"221 3","pages":"2165 - 2176"},"PeriodicalIF":1.0,"publicationDate":"2024-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142890424","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
Groups of diagonal gates in the Clifford hierarchy 克利福德层次结构中的对角门组
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-12-25 DOI: 10.1134/S0040577924120018
Lingxuan Feng, Shunlong Luo
{"title":"Groups of diagonal gates in the Clifford hierarchy","authors":"Lingxuan Feng,&nbsp;Shunlong Luo","doi":"10.1134/S0040577924120018","DOIUrl":"10.1134/S0040577924120018","url":null,"abstract":"<p> The Clifford hierarchy plays a crucial role in the stabilizer formalism of quantum error correction and quantum computation. Apart form the zeroth level (the discrete Heisenberg–Weyl group) and the first level (the Clifford group), all other levels of the Clifford hierarchy are not groups. However, the diagonal gates at all levels do form groups, and it is desirable to characterize their generators and structures. In this paper, we study the diagonal gates at the second level of the Clifford hierarchy. For this, we introduce the notion of a <span>(T)</span>-gate in an arbitrary dimension, generalizing the corresponding notion in prime dimensions. By the use of the <span>(T)</span>-gate, we are able to completely characterize the group structures of the diagonal gates at the second level of the Clifford hierarchy in any (not necessarily prime) dimension. It turns out that the classification depends crucially on the number-theoretic nature of the dimension. The results highlight the special role of the first two primes, <span>(2)</span> and <span>(3)</span>, in the prime factorization of the dimension. The <span>(T)</span>-gate in an arbitrary dimension, apart from its key role as a generator of the diagonal gates, may have independent interest and further applications in quantum theory. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"221 3","pages":"2007 - 2021"},"PeriodicalIF":1.0,"publicationDate":"2024-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889916","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
New similarity reductions and exact solutions of the Date–Jimbo–Kashiwara–Miwa equation Date-Jimbo-Kashiwara-Miwa方程的新相似性约简和精确解
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-12-25 DOI: 10.1134/S0040577924120055
Dongwei Ran, Shaowei Liu
{"title":"New similarity reductions and exact solutions of the Date–Jimbo–Kashiwara–Miwa equation","authors":"Dongwei Ran,&nbsp;Shaowei Liu","doi":"10.1134/S0040577924120055","DOIUrl":"10.1134/S0040577924120055","url":null,"abstract":"<p> We study the <span>((2+1))</span>-dimensional nonlinear Date–Jimbo–Kashiwara–Miwa (DJKM) equation by the CK direct method. In the literature, no one has used the CK direct method to solve the DJKM equation. However, in the process of solving the DJKM equation by the CK direct method, it is almost impossible to solve for all <span>(beta)</span> and <span>(z)</span>, and we therefore use a certain method to find the concrete expressions of <span>(beta)</span> and <span>(z)</span> more easily. Finally, some new one-dimensional similarity reductions and new exact solutions of the DJKM equation are obtained via a large amount of complex and tedious calculations; these solutions can contain some arbitrary functions of <span>(t)</span>. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"221 3","pages":"2062 - 2082"},"PeriodicalIF":1.0,"publicationDate":"2024-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142890488","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
Generating quantum dynamical mappings 生成量子动力学映射
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-12-25 DOI: 10.1134/S0040577924120122
R. N. Gumerov, R. L. Khazhin
{"title":"Generating quantum dynamical mappings","authors":"R. N. Gumerov,&nbsp;R. L. Khazhin","doi":"10.1134/S0040577924120122","DOIUrl":"10.1134/S0040577924120122","url":null,"abstract":"<p> We consider one-parameter families of generating quantum channels. Such families are called the generating quantum dynamical mappings or the generating quantum processes. By the generating channels of composite quantum systems, we understand the channels that allow the channels of constituent subsystems, called the induced channels, to be uniquely defined. Using the criterion for generating and induced linear mappings, we study the properties of bijective quantum channels and the properties of quantum processes consisting of such channels. Using a generating quantum dynamical mapping, we naturally construct the induced dynamical mapping. We show that the properties of continuity and completely positive divisibility of generating quantum dynamical mappings are hereditary for induced dynamical mappings. As an application of the obtained results, we construct continuous completely positive evolutions. For generating quantum dynamical mappings taking values in the set of phase-damping channels, we obtain a criterion for the completely positive divisibility. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"221 3","pages":"2177 - 2192"},"PeriodicalIF":1.0,"publicationDate":"2024-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142890423","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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