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On nonintegrability of three-dimensional Ising model 论三维伊辛模型的不可控性
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-06-01 DOI: 10.1016/S0034-4877(24)00037-5
Wojciech Niedziółka, Jacek Wojtkiewicz
{"title":"On nonintegrability of three-dimensional Ising model","authors":"Wojciech Niedziółka,&nbsp;Jacek Wojtkiewicz","doi":"10.1016/S0034-4877(24)00037-5","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00037-5","url":null,"abstract":"<div><p>It is well known that the partition function of two-dimensional Ising model can be expressed as a Grassmann integral over the action bilinear in Grassmann variables. The key aspect of the proof of this equivalence is to show that all polygons, appearing in Grassmann integration, enter with fixed sign. For three-dimensional model, the partition function can also be expressed by Grassmann integral. However, the action resulting from low-temperature (L-T) expansion contains quartic terms, which do not allow explicit computation of the integral. We wanted to check — apparently not explored — the possibility that using the high-temperature (H-T) expansion would result in action with only bilinear terms (in two dimensions, L-T and H-T expansions are equivalent, but in three dimensions, they differ from each other). It turned out, however, that polygons obtained by Grassmann integration are not of fixed sign for any ordering of Grassmann variables on sites. This way, it is not possible to express the partition function of three-dimensional Ising model as a Grassmann integral over bilinear action.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"93 3","pages":"Pages 271-285"},"PeriodicalIF":1.0,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141487045","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
Conservation laws and nonexistence of local Hamiltonian structures for generalized Infeld—Rowlands equation 广义因费尔德-罗兰兹方程的守恒定律和局部哈密顿结构的不存在性
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-06-01 DOI: 10.1016/S0034-4877(24)00038-7
Jakub Vašíček
{"title":"Conservation laws and nonexistence of local Hamiltonian structures for generalized Infeld—Rowlands equation","authors":"Jakub Vašíček","doi":"10.1016/S0034-4877(24)00038-7","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00038-7","url":null,"abstract":"<div><p>For a certain natural generalization of the Infeld—Rowlands equation we prove nonexistence of nontrivial local Hamiltonian structures and nontrivial local symplectic structures of any order, as well as of nontrivial local Noether and nontrivial local inverse Noether operators of any order, and exhaustively characterize all cases when the equation in question admits nontrivial local conservation laws of any order; the method of establishing the above nonexistence results can be readily applied to many other PDEs.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"93 3","pages":"Pages 287-300"},"PeriodicalIF":1.0,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141483876","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
The nonisospectral super integrable hierarchies associated with Lie superalgebraSL (1, 2) 与李超代数SL (1, 2) 相关的非等谱超可积分层次结构
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-06-01 DOI: 10.1016/S0034-4877(24)00041-7
Si-Yu Gao, Bai-Ying He
{"title":"The nonisospectral super integrable hierarchies associated with Lie superalgebra\u0000S\u0000L (1, 2)","authors":"Si-Yu Gao,&nbsp;Bai-Ying He","doi":"10.1016/S0034-4877(24)00041-7","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00041-7","url":null,"abstract":"<div><p>Based on Lie superalgebra sI(1, 2) and the TAH scheme, we derive (1+1)-dimensional and (2+1)-dimensional nonisospectral integrable hierarchies and the corresponding super Hamiltonian structures. At the same time, we construct a generalized Lie superalgebra sI(1, 2), and apply it to (1+1)-dimensional and (2+1)-dimensional integrable systems. Finally, we discuss the super Hamiltonian structures of (1+1)-dimensional and (2+1)-dimensional integrable hierarchies associated with Lie superalgebra\u0000<span><math><mi>G</mi></math></span>sI(1, 2).</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"93 3","pages":"Pages 327-351"},"PeriodicalIF":1.0,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141483879","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
Index 索引
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-06-01 DOI: 10.1016/S0034-4877(24)00045-4
{"title":"Index","authors":"","doi":"10.1016/S0034-4877(24)00045-4","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00045-4","url":null,"abstract":"","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"93 3","pages":"Pages 393-394"},"PeriodicalIF":1.0,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0034487724000454/pdfft?md5=d2d49aef699b64b4b48f473b989fa096&pid=1-s2.0-S0034487724000454-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141483874","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
Differential geometry of the quantum supergroup GLH,H′ (1|1) 量子超群 GLH,H′ (1|1) 的微分几何学
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-06-01 DOI: 10.1016/S0034-4877(24)00044-2
Salih Celik, Ilknur Temli
{"title":"Differential geometry of the quantum supergroup GLH,H′ (1|1)","authors":"Salih Celik,&nbsp;Ilknur Temli","doi":"10.1016/S0034-4877(24)00044-2","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00044-2","url":null,"abstract":"<div><p>In this paper, we construct a bi-covariant (<em>h,h′</em>)-deformed differential calculus on the Hopf superalgebra of functions on the quantum supergroup GL<sub><em>h.h</em>′</sub> (1|1) and obtain an extended differential calculus (Cartan calculus) by including inner derivations and Lie derivatives. In doing so, we use left-Cartan-Maurer 1-forms and left-vector fields.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"93 3","pages":"Pages 371-391"},"PeriodicalIF":1.0,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141482854","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
IDENTIFYING DIFFUSION CONCENTRATION AND SOURCE TERM FOR ANOMALOUS DIFFUSION EQUATION 确定异常扩散方程的扩散浓度和源项
IF 0.8 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-04-01 DOI: 10.1016/S0034-4877(24)00023-5
Asim Ilyas, Salman A. Malik, Kamran Suhaib
{"title":"IDENTIFYING DIFFUSION CONCENTRATION AND SOURCE TERM FOR ANOMALOUS DIFFUSION EQUATION","authors":"Asim Ilyas,&nbsp;Salman A. Malik,&nbsp;Kamran Suhaib","doi":"10.1016/S0034-4877(24)00023-5","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00023-5","url":null,"abstract":"<div><p>We consider an inverse problem for diffusion equation involving fractional Laplacian operator in space and Hilfer fractional derivatives in time with Dirichlet zero boundary conditions. The inverse problem is to recover time-dependent source term and diffusion concentration with an integral type over-determination condition. We discuss the analytical solution of the inverse problem and prove the existence and uniqueness of the analytical solution. Some special cases and examples for the considered inverse problem are provided.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"93 2","pages":"Pages 145-163"},"PeriodicalIF":0.8,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140880224","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 SOLITON-LIKE SOLUTIONS OF THE REFINED MODEL OF ELASTIC MEDIA CONTAINING INCLUSIONS 关于含有夹杂物的弹性介质细化模型的孤子类解法
IF 0.8 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-04-01 DOI: 10.1016/S0034-4877(24)00024-7
Lucjan Sapa, Sergii Skurativskyi, Vsevolod Vladimirov
{"title":"ON THE SOLITON-LIKE SOLUTIONS OF THE REFINED MODEL OF ELASTIC MEDIA CONTAINING INCLUSIONS","authors":"Lucjan Sapa,&nbsp;Sergii Skurativskyi,&nbsp;Vsevolod Vladimirov","doi":"10.1016/S0034-4877(24)00024-7","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00024-7","url":null,"abstract":"<div><p>A model of nonlinear elastic media containing cavities, microcracks, or soft inclusions is considered. We propose a modification of the well-known model to such media. The modification consists in taking into account those terms in the approximate equation of state that were discarded in the previously considered models. The main goal of the ongoing research is to show the persistence of the soliton-like solutions in the modified model, and to study their dynamical properties.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"93 2","pages":"Pages 165-177"},"PeriodicalIF":0.8,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140880225","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
QUANTUM REVIVALS AND FRACTALITY FOR THE SCHRÖDINGER EQUATION 薛定谔方程的量子复兴与分形
IF 0.8 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-04-01 DOI: 10.1016/S0034-4877(24)00022-3
Gunwoo Cho, Jimyeong Kim, Ihyeok Seo, Seongyeon Kim, Yehyun Kwon
{"title":"QUANTUM REVIVALS AND FRACTALITY FOR THE SCHRÖDINGER EQUATION","authors":"Gunwoo Cho,&nbsp;Jimyeong Kim,&nbsp;Ihyeok Seo,&nbsp;Seongyeon Kim,&nbsp;Yehyun Kwon","doi":"10.1016/S0034-4877(24)00022-3","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00022-3","url":null,"abstract":"<div><p>We investigate the behavior of the Schrödinger equation under the influence of potentials, focusing on its relationship to quantum revivals and fractality. Our findings reveal that the solution displays fractal behavior at irrational times, while exhibiting regularity similar to the initial data at rational times. These extend the results of Oskolkov [<span>16</span>] and Rodnianski [<span>18</span>] on the free Schrödinger evolution to the general case regarding potentials.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"93 2","pages":"Pages 129-143"},"PeriodicalIF":0.8,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140880213","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
CHAIN TRANSITIVITY AND SHADOWING PROPERTY IN QUANTUM DYNAMICAL SYSTEMS 量子动力学系统中的链传递性和阴影特性
IF 0.8 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-04-01 DOI: 10.1016/S0034-4877(24)00026-0
Mona Khare, Ravi Singh Chauhan
{"title":"CHAIN TRANSITIVITY AND SHADOWING PROPERTY IN QUANTUM DYNAMICAL SYSTEMS","authors":"Mona Khare,&nbsp;Ravi Singh Chauhan","doi":"10.1016/S0034-4877(24)00026-0","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00026-0","url":null,"abstract":"<div><p>In the present paper we investigate the notions of chain transitivity, ε-shadowing and expansiveness in the dynamics of quantum measure spaces (<em>P</em>, μ). Besides of several results proved for a chain transitive quantum dynamical system, it is shown that if a measure preserving morphism φ on (<em>P</em>, μ) is chain mixing, then φ<sup><em>n</em></sup> is chain transitive for each <em>n</em> ∊ ℕ. The present study also elucidates interrelationship between ε-shadowing and expansiveness of a quantum dynamical system (<em>P</em>, μ, φ) under suitable conditions. Examples are given to support the theory.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"93 2","pages":"Pages 195-211"},"PeriodicalIF":0.8,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140880208","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
SINGULAR REDUCTION OF CONTACT HAMILTONIAN SYSTEMS 接触哈密顿系统的奇异还原
IF 0.8 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2024-04-01 DOI: 10.1016/S0034-4877(24)00029-6
Qianqian Xia
{"title":"SINGULAR REDUCTION OF CONTACT HAMILTONIAN SYSTEMS","authors":"Qianqian Xia","doi":"10.1016/S0034-4877(24)00029-6","DOIUrl":"https://doi.org/10.1016/S0034-4877(24)00029-6","url":null,"abstract":"<div><p>We study singular reduction of contact Hamiltonian systems acted upon properly by a Lie group. The tools we use are the category of differential space.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"93 2","pages":"Pages 241-260"},"PeriodicalIF":0.8,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140880211","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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