Mathematical Physics, Analysis and Geometry最新文献

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Box and Ball System with Numbered Boxes 带编号盒子的盒子和球系统
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2022-04-24 DOI: 10.1007/s11040-022-09425-6
Yusaku Yamamoto, Akiko Fukuda, Sonomi Kakizaki, Emiko Ishiwata, Masashi Iwasaki, Yoshimasa Nakamura
{"title":"Box and Ball System with Numbered Boxes","authors":"Yusaku Yamamoto,&nbsp;Akiko Fukuda,&nbsp;Sonomi Kakizaki,&nbsp;Emiko Ishiwata,&nbsp;Masashi Iwasaki,&nbsp;Yoshimasa Nakamura","doi":"10.1007/s11040-022-09425-6","DOIUrl":"10.1007/s11040-022-09425-6","url":null,"abstract":"<div><p>The box and ball system (BBS) models the dynamics of balls moving among an array of boxes. The simplest BBS is derived from the ultradiscretization of the discrete Toda equation, which is one of the most famous discrete integrable systems. The discrete Toda equation can be extended to two types of discrete hungry Toda (dhToda) equations, one of which is the equation of motion of the BBS with numbered balls (nBBS). In this paper, based on the ultradiscretization of the other type of dhToda equation, we present a new nBBS in which not balls, but boxes, are numbered. We also investigate conserved quantities with respect to balls and boxes, the solitonical nature of ball motions, and a scattering rule in collisions of balls to clarify the characteristics of the resulting nBBS.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"25 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49337228","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: 0
Bose–Einstein Condensation with Optimal Rate for Trapped Bosons in the Gross–Pitaevskii Regime Gross-Pitaevskii体系中捕获玻色子的最优速率玻色-爱因斯坦凝聚
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2022-04-12 DOI: 10.1007/s11040-022-09424-7
Christian Brennecke, Benjamin Schlein, Severin Schraven
{"title":"Bose–Einstein Condensation with Optimal Rate for Trapped Bosons in the Gross–Pitaevskii Regime","authors":"Christian Brennecke,&nbsp;Benjamin Schlein,&nbsp;Severin Schraven","doi":"10.1007/s11040-022-09424-7","DOIUrl":"10.1007/s11040-022-09424-7","url":null,"abstract":"<div><p>We consider a Bose gas consisting of <i>N</i> particles in <span>({mathbb {R}}^3)</span>, trapped by an external field and interacting through a two-body potential with scattering length of order <span>(N^{-1})</span>. We prove that low energy states exhibit complete Bose–Einstein condensation with optimal rate, generalizing previous work in Boccato et al. (Commun Math Phys 359(3):975–1026, 2018; 376:1311–1395, 2020), restricted to translation invariant systems. This extends recent results in Nam et al. (Preprint, 2001. arXiv:2001.04364), removing the smallness assumption on the size of the scattering length.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"25 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-022-09424-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4484571","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 22
A ({mathbb {Z}}_{2})-Topological Index for Quasi-Free Fermions 准自由费米子的({mathbb {Z}}_{2}) -拓扑指数
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2022-03-14 DOI: 10.1007/s11040-022-09421-w
N. J. B. Aza, A. F. Reyes-Lega, L. A. M. Sequera
{"title":"A ({mathbb {Z}}_{2})-Topological Index for Quasi-Free Fermions","authors":"N. J. B. Aza,&nbsp;A. F. Reyes-Lega,&nbsp;L. A. M. Sequera","doi":"10.1007/s11040-022-09421-w","DOIUrl":"10.1007/s11040-022-09421-w","url":null,"abstract":"<div><p>We use infinite dimensional self-dual <span>(mathrm {CAR})</span> <span>(C^{*})</span>-algebras to study a <span>({mathbb {Z}}_{2})</span>-index, which classifies free-fermion systems embedded on <span>({mathbb {Z}}^{d})</span> disordered lattices. Combes–Thomas estimates are pivotal to show that the <span>({mathbb {Z}}_{2})</span>-index is uniform with respect to the size of the system. We additionally deal with the set of ground states to completely describe the mathematical structure of the underlying system. Furthermore, the weak<span>(^{*})</span>-topology of the set of linear functionals is used to analyze paths connecting different sets of ground states.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"25 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4584348","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
Weyl’s Laws and Connes’ Integration Formulas for Matrix-Valued (L!log !L)-Orlicz Potentials 矩阵值(L!log !L) -Orlicz势的Weyl定律和Connes积分公式
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2022-03-12 DOI: 10.1007/s11040-022-09422-9
Raphaël Ponge
{"title":"Weyl’s Laws and Connes’ Integration Formulas for Matrix-Valued (L!log !L)-Orlicz Potentials","authors":"Raphaël Ponge","doi":"10.1007/s11040-022-09422-9","DOIUrl":"10.1007/s11040-022-09422-9","url":null,"abstract":"<div><p>Thanks to the Birman-Schwinger principle, Weyl’s laws for Birman-Schwinger operators yields semiclassical Weyl’s laws for the corresponding Schrödinger operators. In a recent preprint Rozenblum established quite general Weyl’s laws for Birman-Schwinger operators associated with pseudodifferential operators of critical order and potentials that are product of <span>(L!log !L)</span>-Orlicz functions and Alfhors-regular measures supported on a submanifold. In this paper, we show that, for matrix-valued <span>(L!log !L)</span>-Orlicz potentials supported on the whole manifold, Rozenblum’s results are direct consequences of the Cwikel-type estimates on tori recently established by Sukochev–Zanin. As applications we obtain CLR-type inequalities and semiclassical Weyl’s laws for critical Schrödinger operators associated with matrix-valued <span>(L!log !L)</span>-Orlicz potentials. Finally, we explain how the Weyl’s laws of this paper imply a strong version of Connes’ integration formula for matrix-valued <span>(L!log !L)</span>-Orlicz potentials.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"25 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-022-09422-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4501718","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
Regularising Transformations for Complex Differential Equations with Movable Algebraic Singularities 具有可动代数奇点的复微分方程的正则变换
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2022-03-06 DOI: 10.1007/s11040-022-09417-6
Thomas Kecker, Galina Filipuk
{"title":"Regularising Transformations for Complex Differential Equations with Movable Algebraic Singularities","authors":"Thomas Kecker,&nbsp;Galina Filipuk","doi":"10.1007/s11040-022-09417-6","DOIUrl":"10.1007/s11040-022-09417-6","url":null,"abstract":"<div><p>In a 1979 paper, Okamoto introduced the space of initial values for the six Painlevé equations and their associated Hamiltonian systems, showing that these define regular initial value problems at every point of an augmented phase space, a rational surface with certain exceptional divisors removed. We show that the construction of the space of initial values remains meaningful for certain classes of second-order complex differential equations, and more generally, Hamiltonian systems, where all movable singularities of all their solutions are algebraic poles (by some authors denoted the quasi-Painlevé property), which is a generalisation of the Painlevé property. The difference here is that the initial value problems obtained in the extended phase space become regular only after an additional change of dependent and independent variables. Constructing the analogue of space of initial values for these equations in this way also serves as an algorithm to single out, from a given class of equations or system of equations, those equations which are free from movable logarithmic branch points.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"25 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-022-09417-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4264894","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
J-Trajectories in 4-Dimensional Solvable Lie Group (mathrm {Sol}_0^4) 四维可解李群中的j -轨迹 (mathrm {Sol}_0^4)
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2022-03-06 DOI: 10.1007/s11040-022-09418-5
Zlatko Erjavec, Jun-ichi Inoguchi
{"title":"J-Trajectories in 4-Dimensional Solvable Lie Group (mathrm {Sol}_0^4)","authors":"Zlatko Erjavec,&nbsp;Jun-ichi Inoguchi","doi":"10.1007/s11040-022-09418-5","DOIUrl":"10.1007/s11040-022-09418-5","url":null,"abstract":"<div><p><i>J</i>-trajectories are arc length parameterized curves in almost Hermitian manifold which satisfy the equation <span>(nabla _{{dot{gamma }}}{dot{gamma }}=q J {dot{gamma }})</span>. In this paper <i>J</i>-trajectories in the solvable Lie group <span>(mathrm {Sol}_0^4)</span> are investigated. The first and the second curvature of a non-geodesic <i>J</i>-trajectory in an arbitrary LCK manifold whose anti Lee field has constant length are examined. In particular, the curvatures of non-geodesic <i>J</i>-trajectories in <span>(mathrm {Sol}_0^4)</span> are characterized.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"25 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4263037","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
On Tsallis and Kaniadakis Divergences 关于Tsallis和Kaniadakis分歧
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2022-02-24 DOI: 10.1007/s11040-022-09420-x
Răzvan-Cornel Sfetcu, Sorina-Cezarina Sfetcu, Vasile Preda
{"title":"On Tsallis and Kaniadakis Divergences","authors":"Răzvan-Cornel Sfetcu,&nbsp;Sorina-Cezarina Sfetcu,&nbsp;Vasile Preda","doi":"10.1007/s11040-022-09420-x","DOIUrl":"10.1007/s11040-022-09420-x","url":null,"abstract":"<div><p>We study some properties concerning Tsallis and Kaniadakis divergences between two probability measures. More exactly, we prove the pseudo-additivity, non-negativity, monotonicity and find some bounds for the divergences mentioned above.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"25 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-022-09420-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4545593","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
Factorization Problems on Rational Loop Groups, and the Poisson Geometry of Yang-Baxter Maps 有理环群上的因式分解问题及Yang-Baxter映射的泊松几何
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2022-02-19 DOI: 10.1007/s11040-022-09419-4
Luen-Chau Li
{"title":"Factorization Problems on Rational Loop Groups, and the Poisson Geometry of Yang-Baxter Maps","authors":"Luen-Chau Li","doi":"10.1007/s11040-022-09419-4","DOIUrl":"10.1007/s11040-022-09419-4","url":null,"abstract":"<div><p>The study of set-theoretic solutions of the Yang-Baxter equation, also known as Yang-Baxter maps, is historically a meeting ground for various areas of mathematics and mathematical physics. In this work, we study factorization problems on rational loop groups, which give rise to Yang-Baxter maps on various geometrical objects. We also study the symplectic and Poisson geometry of these Yang-Baxter maps, which we show to be integrable maps in the sense of having natural collections of Poisson commuting integrals. In a special case, the factorization problems we consider are associated with the <i>N</i>-soliton collision process in the <i>n</i>-Manakov system, and in this context we show that the polarization scattering map is a symplectomorphism.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"25 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4750587","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
Involutions of Halphen Pencils of Index 2 and Discrete Integrable Systems 指数2与离散可积系统的Halphen铅笔的对合
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2022-02-05 DOI: 10.1007/s11040-022-09416-7
Kangning Wei
{"title":"Involutions of Halphen Pencils of Index 2 and Discrete Integrable Systems","authors":"Kangning Wei","doi":"10.1007/s11040-022-09416-7","DOIUrl":"10.1007/s11040-022-09416-7","url":null,"abstract":"<div><p>We constructed involutions for a Halphen pencil of index 2, and proved that the birational mapping corresponding to the autonomous reduction of the elliptic Painlevé equation for the same pencil can be obtained as the composition of two such involutions.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"25 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-022-09416-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4207410","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Phase Transitions and Percolation at Criticality in Enhanced Random Connection Models 增强随机连接模型中的相变和临界渗流
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2022-01-13 DOI: 10.1007/s11040-021-09409-y
Srikanth K. Iyer, Sanjoy Kr. Jhawar
{"title":"Phase Transitions and Percolation at Criticality in Enhanced Random Connection Models","authors":"Srikanth K. Iyer,&nbsp;Sanjoy Kr. Jhawar","doi":"10.1007/s11040-021-09409-y","DOIUrl":"10.1007/s11040-021-09409-y","url":null,"abstract":"<div><p>We study phase transition and percolation at criticality for three random graph models on the plane, viz., the homogeneous and inhomogeneous enhanced random connection models (RCM) and the Poisson stick model. These models are built on a homogeneous Poisson point process <span>(mathcal {P}_{lambda })</span> in <span>(mathbb {R}^{2})</span> of intensity <i>λ</i>. In the homogeneous RCM, the vertices at <i>x</i>,<i>y</i> are connected with probability <i>g</i>(|<i>x</i> − <i>y</i>|), independent of everything else, where <span>(g:[0,infty ) to [0,1])</span> and |⋅| is the Euclidean norm. In the inhomogeneous version of the model, points of <span>(mathcal {P}_{lambda })</span> are endowed with weights that are non-negative independent random variables with distribution <span>(P(W&gt;w)= w^{-beta }1_{[1,infty )}(w))</span>, <i>β</i> &gt; 0. Vertices located at <i>x</i>,<i>y</i> with weights <i>W</i><sub><i>x</i></sub>,<i>W</i><sub><i>y</i></sub> are connected with probability <span>(1 - exp left (- frac {eta W_{x}W_{y}}{|x-y|^{alpha }} right ))</span>, <i>η</i>,<i>α</i> &gt; 0, independent of all else. The graphs are enhanced by considering the edges of the graph as straight line segments starting and ending at points of <span>(mathcal {P}_{lambda })</span>. A path in the graph is a continuous curve that is a subset of the union of all these line segments. The Poisson stick model consists of line segments of independent random lengths and orientation with the mid point of each segment located at a distinct point of <span>(mathcal {P}_{lambda })</span>. Intersecting lines form a path in the graph. A graph is said to percolate if there is an infinite connected component or path. We derive conditions for the existence of a phase transition and show that there is no percolation at criticality.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"25 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-021-09409-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4533842","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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