发布求助
文献互助 智能选刊 最新文献

Mathematical Physics, Analysis and Geometry最新文献

筛选
英文 中文
Discrete mKdV Equation via Darboux Transformation 基于达布变换的离散mKdV方程
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2021-07-14 DOI: 10.1007/s11040-021-09398-y
Joseph Cho, Wayne Rossman, Tomoya Seno
{"title":"Discrete mKdV Equation via Darboux Transformation","authors":"Joseph Cho,&nbsp;Wayne Rossman,&nbsp;Tomoya Seno","doi":"10.1007/s11040-021-09398-y","DOIUrl":"10.1007/s11040-021-09398-y","url":null,"abstract":"<div><p>We introduce an efficient route to obtaining the discrete potential mKdV equation emerging from a particular discrete motion of discrete planar curves.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s11040-021-09398-y","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4000475","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Asymptotic Behavior of Density in the Boundary-Driven Exclusion Process on the Sierpinski Gasket Sierpinski垫片边界驱动不相容过程中密度的渐近行为
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2021-07-08 DOI: 10.1007/s11040-021-09392-4
Joe P. Chen, Patrícia Gonçalves
{"title":"Asymptotic Behavior of Density in the Boundary-Driven Exclusion Process on the Sierpinski Gasket","authors":"Joe P. Chen,&nbsp;Patrícia Gonçalves","doi":"10.1007/s11040-021-09392-4","DOIUrl":"10.1007/s11040-021-09392-4","url":null,"abstract":"<div><p>We derive the macroscopic laws that govern the evolution of the density of particles in the exclusion process on the Sierpinski gasket in the presence of a variable speed boundary. We obtain, at the hydrodynamics level, the heat equation evolving on the Sierpinski gasket with either Dirichlet or Neumann boundary conditions, depending on whether the reservoirs are fast or slow. For a particular strength of the boundary dynamics we obtain linear Robin boundary conditions. As for the fluctuations, we prove that, when starting from the stationary measure, namely the product Bernoulli measure in the equilibrium setting, they are governed by Ornstein-Uhlenbeck processes with the respective boundary conditions.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s11040-021-09392-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4339805","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Convergence of Discrete Period Matrices and Discrete Holomorphic Integrals for Ramified Coverings of the Riemann Sphere 黎曼球分支覆盖的离散周期矩阵和离散全纯积分的收敛性
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2021-07-02 DOI: 10.1007/s11040-021-09394-2
Alexander I. Bobenko, Ulrike Bücking
{"title":"Convergence of Discrete Period Matrices and Discrete Holomorphic Integrals for Ramified Coverings of the Riemann Sphere","authors":"Alexander I. Bobenko,&nbsp;Ulrike Bücking","doi":"10.1007/s11040-021-09394-2","DOIUrl":"10.1007/s11040-021-09394-2","url":null,"abstract":"<div><p>We consider the class of compact Riemann surfaces which are ramified coverings of the Riemann sphere <span>(hat {mathbb {C}})</span>. Based on a triangulation of this covering we define discrete (multivalued) harmonic and holomorphic functions. We prove that the corresponding discrete period matrices converge to their continuous counterparts. In order to achieve an error estimate, which is linear in the maximal edge length of the triangles, we suitably adapt the triangulations in a neighborhood of every branch point. Finally, we also prove a convergence result for discrete holomorphic integrals for our adapted triangulations of the ramified covering.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s11040-021-09394-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4087019","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Wegner Estimate for Random Divergence-Type Operators Monotone in the Randomness 随机发散型算子单调的Wegner估计
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2021-06-19 DOI: 10.1007/s11040-021-09396-0
Alexander Dicke
{"title":"Wegner Estimate for Random Divergence-Type Operators Monotone in the Randomness","authors":"Alexander Dicke","doi":"10.1007/s11040-021-09396-0","DOIUrl":"10.1007/s11040-021-09396-0","url":null,"abstract":"<div><p>In this note, a Wegner estimate for random divergence-type operators that are monotone in the randomness is proven. The proof is based on a recently shown unique continuation estimate for the gradient and the ensuing eigenvalue liftings. The random model which is studied here contains quite general random perturbations, among others, some that have a non-linear dependence on the random parameters.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s11040-021-09396-0","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4756699","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Boundary from Bulk Integrability in Three Dimensions: 3D Reflection Maps from Tetrahedron Maps 三维体可积性边界:四面体映射的三维反射映射
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2021-06-18 DOI: 10.1007/s11040-021-09393-3
Akihito Yoneyama
{"title":"Boundary from Bulk Integrability in Three Dimensions: 3D Reflection Maps from Tetrahedron Maps","authors":"Akihito Yoneyama","doi":"10.1007/s11040-021-09393-3","DOIUrl":"10.1007/s11040-021-09393-3","url":null,"abstract":"<div><p>We establish a general method for obtaining set-theoretical solutions to the 3D reflection equation by using known ones to the Zamolodchikov tetrahedron equation, where the former equation was proposed by Isaev and Kulish as a boundary analog of the latter. By applying our method to Sergeev’s electrical solution and a two-component solution associated with the discrete modified KP equation, we obtain new solutions to the 3D reflection equation. Our approach is closely related to a relation between the transition maps of Lusztig’s parametrizations of the totally positive part of <i>S</i><i>L</i><sub>3</sub> and <i>S</i><i>O</i><sub>5</sub>, which is obtained via folding the Dynkin diagram of <i>A</i><sub>3</sub> into one of <i>B</i><sub>2</sub>.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s11040-021-09393-3","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4723758","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
On the Prequantisation Map for 2-Plectic Manifolds 关于2-塑性流形的预量化映射
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2021-06-05 DOI: 10.1007/s11040-021-09391-5
Gabriel Sevestre, Tilmann Wurzbacher
{"title":"On the Prequantisation Map for 2-Plectic Manifolds","authors":"Gabriel Sevestre,&nbsp;Tilmann Wurzbacher","doi":"10.1007/s11040-021-09391-5","DOIUrl":"https://doi.org/10.1007/s11040-021-09391-5","url":null,"abstract":"<p>For a manifold <i>M</i> with an integral closed 3-form <i>ω</i>, we construct a <i>P</i><i>U</i>(<i>H</i>)-bundle and a Lie groupoid over its total space, together with a curving in the sense of gerbes. If the form is non-degenerate, we furthermore give a natural Lie 2-algebra quasi-isomorphism from the observables of (<i>M</i>, <i>ω</i>) to the weak symmetries of the above geometric structure, generalising the prequantisation map of Kostant and Souriau.</p>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s11040-021-09391-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4215689","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
Renormalization in Combinatorially Non-Local Field Theories: The Hopf Algebra of 2-Graphs 组合非局部场论中的重整化:2-图的Hopf代数
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2021-05-28 DOI: 10.1007/s11040-021-09390-6
Johannes Thürigen
{"title":"Renormalization in Combinatorially Non-Local Field Theories: The Hopf Algebra of 2-Graphs","authors":"Johannes Thürigen","doi":"10.1007/s11040-021-09390-6","DOIUrl":"https://doi.org/10.1007/s11040-021-09390-6","url":null,"abstract":"<p>Renormalization in perturbative quantum field theory is based on a Hopf algebra of Feynman diagrams. A precondition for this is locality. Therefore one might suspect that non-local field theories such as matrix or tensor field theories cannot benefit from a similar algebraic understanding. Here I show that, on the contrary, perturbative renormalization of a broad class of such field theories is based in the same way on a Hopf algebra. Their interaction vertices have the structure of graphs. This gives the necessary concept of locality and leads to Feynman diagrams defined as “2-graphs” which generate the Hopf algebra. These results set the stage for a systematic study of perturbative renormalization as well as non-perturbative aspects, e.g. Dyson-Schwinger equations, for a number of combinatorially non-local field theories with possible applications to random geometry and quantum gravity.</p>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s11040-021-09390-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5092665","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
The Analytic Evolution of Dyson–Schwinger Equations via Homomorphism Densities Dyson-Schwinger方程的同态密度解析演化
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2021-05-20 DOI: 10.1007/s11040-021-09389-z
Ali Shojaei-Fard
{"title":"The Analytic Evolution of Dyson–Schwinger Equations via Homomorphism Densities","authors":"Ali Shojaei-Fard","doi":"10.1007/s11040-021-09389-z","DOIUrl":"https://doi.org/10.1007/s11040-021-09389-z","url":null,"abstract":"<p>Feynman graphon representations of Feynman diagrams lead us to build a new separable Banach space <span>(mathcal {S}^{Phi ,g}_{approx })</span> originated from the collection of all Dyson–Schwinger equations in a given (strongly coupled) gauge field theory <i>Φ</i> with the bare coupling constant <i>g</i>. We study the Gateaux differential calculus on the space of functionals on <span>(mathcal {S}^{Phi ,g}_{approx })</span> in terms of a new class of homomorphism densities. We then show that Taylor series representations of smooth functionals on <span>(mathcal {S}^{Phi ,g}_{approx })</span> provide a new analytic description for solutions of combinatorial Dyson–Schwinger equations.</p>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s11040-021-09389-z","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4799496","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
Long-Time Asymptotics for the Focusing Hirota Equation with Non-Zero Boundary Conditions at Infinity Via the Deift-Zhou Approach 用Deift-Zhou方法求无限远处具有非零边界条件的聚焦Hirota方程的长时间渐近性
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2021-05-08 DOI: 10.1007/s11040-021-09388-0
Shuyan Chen, Zhenya Yan, Boling Guo
{"title":"Long-Time Asymptotics for the Focusing Hirota Equation with Non-Zero Boundary Conditions at Infinity Via the Deift-Zhou Approach","authors":"Shuyan Chen,&nbsp;Zhenya Yan,&nbsp;Boling Guo","doi":"10.1007/s11040-021-09388-0","DOIUrl":"https://doi.org/10.1007/s11040-021-09388-0","url":null,"abstract":"<p>We are concerned with the long-time asymptotic behavior of the solution for the focusing Hirota equation (also called third-order nonlinear Schr?dinger equation) with symmetric, non-zero boundary conditions (NZBCs) at infinity. Firstly, based on the Lax pair with NZBCs, the direct and inverse scattering problems are used to establish the oscillatory Riemann-Hilbert (RH) problem with distinct jump curves. Secondly, the Deift-Zhou nonlinear steepest-descent method is employed to analyze the oscillatory RH problem such that the long-time asymptotic solutions are proposed in two distinct domains of space-time plane (i.e., the plane-wave and modulated elliptic-wave domains), respectively. Finally, the modulation instability of the considered Hirota equation is also investigated.</p>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s11040-021-09388-0","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4356536","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 8
Topological Decompositions of the Pauli Group and their Influence on Dynamical Systems 泡利群的拓扑分解及其对动力系统的影响
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2021-05-06 DOI: 10.1007/s11040-021-09387-1
Fabio Bagarello, Yanga Bavuma, Francesco G. Russo
{"title":"Topological Decompositions of the Pauli Group and their Influence on Dynamical Systems","authors":"Fabio Bagarello,&nbsp;Yanga Bavuma,&nbsp;Francesco G. Russo","doi":"10.1007/s11040-021-09387-1","DOIUrl":"https://doi.org/10.1007/s11040-021-09387-1","url":null,"abstract":"<p>In the present paper we show that it is possible to obtain the well known Pauli group <i>P</i> = 〈<i>X</i>,<i>Y</i>,<i>Z</i> | <i>X</i><sup>2</sup> = <i>Y</i><sup>2</sup> = <i>Z</i><sup>2</sup> =?1,(<i>Y</i> <i>Z</i>)<sup>4</sup> = (<i>Z</i><i>X</i>)<sup>4</sup> = (<i>X</i><i>Y</i> )<sup>4</sup> =?1〉 of order 16 as an appropriate quotient group of two distinct spaces of orbits of the three dimensional sphere <i>S</i><sup>3</sup>. The first of these spaces of orbits is realized via an action of the quaternion group <i>Q</i><sub>8</sub> on <i>S</i><sup>3</sup>; the second one via an action of the cyclic group of order four <span>(mathbb {Z}(4))</span> on <i>S</i><sup>3</sup>. We deduce a result of decomposition of <i>P</i> of topological nature and then we find, in connection with the theory of pseudo-fermions, a possible physical interpretation of this decomposition.</p>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s11040-021-09387-1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4271644","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
首页 上一页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信