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A NONAUTONOMOUS p-ADIC DIFFUSION EQUATION ON TIME CHANGING GRAPHS 时变图上的非自治p进扩散方程
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2025-04-01 DOI: 10.1016/S0034-4877(25)00023-0
PATRICK ERIK BRADLEY, ÁNGEL MORÁN LEDEZMA
{"title":"A NONAUTONOMOUS p-ADIC DIFFUSION EQUATION ON TIME CHANGING GRAPHS","authors":"PATRICK ERIK BRADLEY,&nbsp;ÁNGEL MORÁN LEDEZMA","doi":"10.1016/S0034-4877(25)00023-0","DOIUrl":"10.1016/S0034-4877(25)00023-0","url":null,"abstract":"<div><div>Motivated by the recently proven presence of ultrametricity in physical models (certain spin glasses), the very recent study of Turing patterns on locally ultrametric state spaces, and the study of Turing patterns in time changing networks, first nonautonomous diffusion operators on such systems, where finitely many compact <em>p</em>-adic spaces are joined by a graph structure, are studied, including their Dirichlet and von Neumann eigenvalues. Secondly, the Cauchy problem for the heat equation associated with these operators is solved, its solution approximated by Trotter products, and thirdly, the corresponding Feller property as well as the Markov property (a Hunt process) is established.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"95 2","pages":"Pages 155-180"},"PeriodicalIF":1.0,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144107399","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
Causality in the Maximally Extended Reissner-NordstrÖm Spacetime With Identifications 最大扩展Reissner-NordstrÖm时空中的因果关系
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2025-04-01 DOI: 10.1016/S0034-4877(25)00024-2
Andrzej Krasiński
{"title":"Causality in the Maximally Extended Reissner-NordstrÖm Spacetime With Identifications","authors":"Andrzej Krasiński","doi":"10.1016/S0034-4877(25)00024-2","DOIUrl":"10.1016/S0034-4877(25)00024-2","url":null,"abstract":"<div><div>The maximally extended Reissner-Nordström (RN) spacetime with <em>e</em><sup>2</sup> <em>m</em><sup>2</sup> can be interpreted either as an infinite chain of asymptotically flat regions connected by tunnels between timelike singularities or as a set of just one pair of asymptotically flat regions and one tunnel; the repetitions of this set in the infinite chain being identified. The second interpretation gives rise to the suspicion of acausality, i.e. the possibility of sending messages to one’s own past. A numerical investigation of this problem was carried out in this paper and gave the following result. Let E be the initial point of a radial timelike future-directed ingoing geodesic G, lying halfway between the outer horizon and the image of the null infinity in the maximally extended RN spacetime. Let E’ be the first future copy of E. It was verified whether the turning point of G lies outside or inside the past light cone (PLC) of E′. In the second case the breach of causality does occur. It turned out that the acausality is present when <em>V<sub>E</sub></em>, the timelike coordinate of E, is negative with a sufficiently large |<em>V<sub>E</sub></em>|, and is absent with a sufficiently large <em>V<sub>E</sub></em> &gt; 0. In between these values there exists a \u0000\t\t\t\t<span><math><mrow><msub><mover><mi>V</mi><mo>~</mo></mover><mi>E</mi></msub></mrow></math></span>, dependent on the initial data for the geodesic, for which the turning point lies on the PLC. So, the identification does lead to acausality. Nonradial timelike and null geodesics were also investigated, and a few hitherto unknown properties of the maximal extension were revealed. For example, the singularity arc at <em>r</em> = 0 may be convex or concave, depending on the values of <em>m</em> and <em>e</em>.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"95 2","pages":"Pages 181-214"},"PeriodicalIF":1.0,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144107400","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
Pseudo Z Symmetric Space-Times Admitting a Type of Semi-Symmetric Nonmetric Connection 伪Z对称时空允许一类半对称非度量连接
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2025-02-01 DOI: 10.1016/S0034-4877(25)00009-6
Hülya Bağdatli Yilmaz, Uday Chand De
{"title":"Pseudo Z Symmetric Space-Times Admitting a Type of Semi-Symmetric Nonmetric Connection","authors":"Hülya Bağdatli Yilmaz,&nbsp;Uday Chand De","doi":"10.1016/S0034-4877(25)00009-6","DOIUrl":"10.1016/S0034-4877(25)00009-6","url":null,"abstract":"<div><div>This paper aims at investigating pseudo Z symmetric space-times (PZS)<sub>4</sub> admitting a type of semi-symmetric nonmetric connection (ssnmc). At first, we scrutinize the impact of a ssnmc on Lorentzian manifolds and establish a nontrivial example. Then, we examine the general properties of (PZS)<sub>4</sub> space-times and express the physical consequences of this space-time. Among others, it is demonstrated that a (PZS)<sub>4</sub> space-time admitting a ssnmc whose Ricci tensor vanishes becomes a GRW space-time as well as a perfect fluid space-time and a purely electric space-time under a certain condition.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"95 1","pages":"Pages 39-52"},"PeriodicalIF":1.0,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143680612","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Topology behind Topological Insulators 拓扑绝缘体背后的拓扑
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2025-02-01 DOI: 10.1016/S0034-4877(25)00008-4
Koushik Ray, Siddhartha Sen
{"title":"Topology behind Topological Insulators","authors":"Koushik Ray,&nbsp;Siddhartha Sen","doi":"10.1016/S0034-4877(25)00008-4","DOIUrl":"10.1016/S0034-4877(25)00008-4","url":null,"abstract":"<div><div>In this paper topological <em>K</em>-group calculations for fiber bundles with structure group SO(3) over tori are carried out to explain why topological insulators have special conducting points on their surface but are bulk insulators. It is shown that these special points are gapless and conducting for topological reasons and follow from the <em>K</em>-group calculations. The existence of gapless surface points is established with the help of an additional topological property of the <em>K</em>-groups which relates them to the index theorem of an operator. The index theorem relates zeros of operators to topology. For the topological insulator the relevant operator is a Dirac operator, that emerges in the problem because the system has strong spin-orbit interactions and time reversal invariance. Calculating <em>K</em>-groups over tori require some special topological tools that are not widely known. These are explained. We then show that the actual calculation of <em>K</em>-groups over tori becomes straightforward once a few topological results are in place. Since condensed matter systems with periodic lattices are always bundles over tori the procedures described is of general interest.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"95 1","pages":"Pages 11-37"},"PeriodicalIF":1.0,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143680611","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On HA-Weakly Periodic P-Adic Generalized Gibbs Measures of P-Adic Ising Model with an External Field on a Cayley Tree Cayley树上带外域的p进Ising模型的ha -弱周期p进广义Gibbs测度
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2025-02-01 DOI: 10.1016/S0034-4877(25)00012-6
Muzaffar M. Rahmatullaev, Zulxumor T. Abdukaxorova
{"title":"On HA-Weakly Periodic P-Adic Generalized Gibbs Measures of P-Adic Ising Model with an External Field on a Cayley Tree","authors":"Muzaffar M. Rahmatullaev,&nbsp;Zulxumor T. Abdukaxorova","doi":"10.1016/S0034-4877(25)00012-6","DOIUrl":"10.1016/S0034-4877(25)00012-6","url":null,"abstract":"<div><div>In the present paper, we investigate weakly periodic <em>p</em>-adic generalized Gibbs measures for <em>p</em>-adic Ising model with an external field on the Cayley tree of order two. For a normal subgroup of the group representation of the Cayley tree we prove that there exists at least one unbounded weakly periodic (in particular, nonperiodic) <em>p</em>-adic generalized Gibbs measures for this model. Moreover, we show that if <em>p</em> is any odd prime then a phase transition occurs, if <em>p</em> = 2 then a quasi phase transition occurs for <em>p</em>-adic Ising model with an external field.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"95 1","pages":"Pages 93-109"},"PeriodicalIF":1.0,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143680615","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stability of a Generalized Linear Weingarten Spacelike Hypersurface in Robertson–Walker Spacetimes Robertson-Walker时空中广义线性Weingarten类空间超曲面的稳定性
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2025-02-01 DOI: 10.1016/S0034-4877(25)00013-8
Hyelim Han
{"title":"Stability of a Generalized Linear Weingarten Spacelike Hypersurface in Robertson–Walker Spacetimes","authors":"Hyelim Han","doi":"10.1016/S0034-4877(25)00013-8","DOIUrl":"10.1016/S0034-4877(25)00013-8","url":null,"abstract":"<div><div>In this article, we study the variational problem of maximizing a certain linear combination of area functionals of a closed generalized linear Weingarten spacelike hypersurface <em>M<sup>n</sup></em> immersed in a foliated spacetime \u0000\t\t\t\t<span><math><mrow><msubsup><mover><mi>M</mi><mo>~</mo></mover><mn>1</mn><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msubsup></mrow></math></span>. Given a Robertson-Walker spacetime \u0000\t\t\t\t<span><math><mrow><msubsup><mover><mi>M</mi><mo>~</mo></mover><mn>1</mn><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msubsup><mrow><mo>(</mo><mi>c</mi><mo>)</mo></mrow><mo>=</mo><mi>I</mi><msub><mo>×</mo><mi>ϕ</mi></msub><msup><mi>F</mi><mi>n</mi></msup></mrow></math></span>, we exhibit conditions on <em>M<sup>n</sup></em> which guarantee that (strong) stability is necessary and sufficient for <em>M<sup>n</sup></em> to be totally umbilic. Under a suitable restriction on <em>M<sup>n</sup></em>, we also prove that if a closed generalized linear Weingarten spacelike hypersurface in \u0000\t\t\t\t<span><math><mrow><msubsup><mi>S</mi><mn>1</mn><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msubsup></mrow></math></span> is (strongly) stable, then it must be a totally umbilic round sphere.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"95 1","pages":"Pages 111-128"},"PeriodicalIF":1.0,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143680616","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Families of Differential Equations Associated with The Generalized 1-Parameter 3-Variable Hermite–Frobenius–Euler Polynomials 广义1参数3变量Hermite-Frobenius-Euler多项式相关的微分方程族
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2025-02-01 DOI: 10.1016/S0034-4877(25)00010-2
Shahid Ahmad Wani, Mohra Zayed, Hassan Ali, Subuhi Khan
{"title":"Families of Differential Equations Associated with The Generalized 1-Parameter 3-Variable Hermite–Frobenius–Euler Polynomials","authors":"Shahid Ahmad Wani,&nbsp;Mohra Zayed,&nbsp;Hassan Ali,&nbsp;Subuhi Khan","doi":"10.1016/S0034-4877(25)00010-2","DOIUrl":"10.1016/S0034-4877(25)00010-2","url":null,"abstract":"<div><div>This paper presents a novel framework for introducing generalized 1-parameter 3-variable Hermite–Frobenius–Euler polynomials. These polynomials are characterized by generating functions, series definitions, and summation formulae, elucidating their fundamental properties. Moreover, the study establishes recurrence relations, shift operators, and various differential equations, including differential, integro-differential, and partial differential equations, utilizing a factorization method.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"95 1","pages":"Pages 53-70"},"PeriodicalIF":1.0,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143680613","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Geometric Application of Soliton Surfaces Associated with The Betchov–Da Rios Equation Using an Extended Darboux Frame Field in E4 利用扩展Darboux框架场与Betchov-Da Rios方程相关的孤子曲面在E4中的几何应用
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2025-02-01 DOI: 10.1016/S0034-4877(25)00011-4
Ahmet Kazan, Mustafa Altin
{"title":"A Geometric Application of Soliton Surfaces Associated with The Betchov–Da Rios Equation Using an Extended Darboux Frame Field in E4","authors":"Ahmet Kazan,&nbsp;Mustafa Altin","doi":"10.1016/S0034-4877(25)00011-4","DOIUrl":"10.1016/S0034-4877(25)00011-4","url":null,"abstract":"<div><div>In this paper, for a soliton surface Ω = Ω(<em>u, v</em>) associated with the Betchov–Da Rios equation, we obtain the derivative formulae of an extended Darboux frame field of a unit speed <em>u</em>-parameter curve Ω = Ω(<em>u, v</em>) for all <em>v.</em> Also, we get the geometric invariants <em>k</em> and <em>h</em> of the soliton surface Ω = Ω(<em>u, v</em>) and we obtain the Gaussian curvature, mean curvature vector and Gaussian torsion of Ω. We give some important geometric characterizations such as flatness, minimality and semi-umbilicaly with the aid of these invariants. Additionally, we study the curvature ellipse of the Betchov–Da Rios soliton surface and Wintgen ideal (superconformal) Betchov–Da Rios soliton surface with respect to an extended Darboux frame field. Finally, we construct an application for the Betchov–Da Rios soliton surface with the aid of an extended Darboux frame field.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"95 1","pages":"Pages 71-92"},"PeriodicalIF":1.0,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143680614","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Imaginarity Measures Induced by Relative Entropy 由相对熵引起的想象性度量
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2025-02-01 DOI: 10.1016/S0034-4877(25)00003-5
Xiangyu Chen, Qiang Lei
{"title":"Imaginarity Measures Induced by Relative Entropy","authors":"Xiangyu Chen,&nbsp;Qiang Lei","doi":"10.1016/S0034-4877(25)00003-5","DOIUrl":"10.1016/S0034-4877(25)00003-5","url":null,"abstract":"<div><div>In this paper, we introduce two measures for the resource theory of imaginarity. One is induced by α-<em>z</em>-Rényi relative entropy and the other, defined for positive-definite density matrices, is induced by Tsallis relative operator entropy. The relationships between different imaginarity measures and their properties are also discussed.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"95 1","pages":"Pages 1-10"},"PeriodicalIF":1.0,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143680672","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Ground states for the potts model with an external field 有外场的波茨模型的基态
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-12-01 DOI: 10.1016/S0034-4877(24)00082-X
Muhayyo A. Rasulova
{"title":"Ground states for the potts model with an external field","authors":"Muhayyo A. Rasulova","doi":"10.1016/S0034-4877(24)00082-X","DOIUrl":"10.1016/S0034-4877(24)00082-X","url":null,"abstract":"<div><div>We consider a <em>(q +</em> 1)-state Potts model with nonzero external field on the Cayley tree. We describe all ground states for this model with a translation-invariant external field and all two-periodic ground states with a periodic external field.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"94 3","pages":"Pages 325-334"},"PeriodicalIF":1.0,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143317063","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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