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Trees and Superintegrable Lotka–Volterra Families 树与超积分洛特卡-伏特拉家族
IF 0.9 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2024-11-26 DOI: 10.1007/s11040-024-09496-7
Peter H. van der Kamp, G. R. W. Quispel, David I. McLaren
{"title":"Trees and Superintegrable Lotka–Volterra Families","authors":"Peter H. van der Kamp,&nbsp;G. R. W. Quispel,&nbsp;David I. McLaren","doi":"10.1007/s11040-024-09496-7","DOIUrl":"10.1007/s11040-024-09496-7","url":null,"abstract":"<div><p>To any tree on <i>n</i> vertices we associate an <i>n</i>-dimensional Lotka–Volterra system with <span>(3n-2)</span> parameters and, for generic values of the parameters, prove it is superintegrable, i.e. it admits <span>(n-1)</span> functionally independent integrals. We also show how each system can be reduced to an (<span>(n-1)</span>)-dimensional system which is superintegrable and solvable by quadratures.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"27 4","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714575","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
Equality of Magnetization and Edge Current for Interacting Lattice Fermions at Positive Temperature 正温下相互作用晶格费米子的磁化和边缘电流相等
IF 0.9 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2024-11-25 DOI: 10.1007/s11040-024-09495-8
Jonas Lampart, Massimo Moscolari, Stefan Teufel, Tom Wessel
{"title":"Equality of Magnetization and Edge Current for Interacting Lattice Fermions at Positive Temperature","authors":"Jonas Lampart,&nbsp;Massimo Moscolari,&nbsp;Stefan Teufel,&nbsp;Tom Wessel","doi":"10.1007/s11040-024-09495-8","DOIUrl":"10.1007/s11040-024-09495-8","url":null,"abstract":"<div><p>We prove that the magnetization is equal to the edge current in the thermodynamic limit for a large class of models of lattice fermions with finite-range interactions satisfying local indistinguishability of the Gibbs state, a condition known to hold for sufficiently high temperatures. Our result implies that edge currents in such systems are determined by bulk properties and are therefore stable against large perturbations near the boundaries. Moreover, the equality persists also after taking the derivative with respect to the chemical potential. We show that this form of bulk-edge correspondence is essentially a consequence of homogeneity in the bulk and locality of the Gibbs state. An important intermediate result is a new version of Bloch’s theorem for two-dimensional systems, stating that persistent currents vanish in the bulk.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"27 4","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-024-09495-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142694728","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
Braided Hopf algebras and gauge transformations 编织霍普夫数组和规整变换
IF 0.9 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2024-11-20 DOI: 10.1007/s11040-024-09492-x
Paolo Aschieri, Giovanni Landi, Chiara Pagani
{"title":"Braided Hopf algebras and gauge transformations","authors":"Paolo Aschieri,&nbsp;Giovanni Landi,&nbsp;Chiara Pagani","doi":"10.1007/s11040-024-09492-x","DOIUrl":"10.1007/s11040-024-09492-x","url":null,"abstract":"<div><p>We study infinitesimal gauge transformations of <i>K</i>-equivariant noncommutative principal bundles, for <i>K</i> a triangular Hopf algebra. They form a Lie algebra of derivations in the category of <i>K</i>-modules. We study Drinfeld twist deformations of these infinitesimal gauge transformations. We give several examples from abelian and Jordanian twist deformations. These include the quantum Lie algebra of gauge transformations of the instanton bundle and of the orthogonal bundle on the quantum sphere <span>(S^4_theta )</span>.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"27 4","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142679594","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
Index of Bipolar Surfaces to Otsuki Tori 双极表面到大月鸟迹的索引
IF 0.9 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2024-11-13 DOI: 10.1007/s11040-024-09494-9
Egor Morozov
{"title":"Index of Bipolar Surfaces to Otsuki Tori","authors":"Egor Morozov","doi":"10.1007/s11040-024-09494-9","DOIUrl":"10.1007/s11040-024-09494-9","url":null,"abstract":"<div><p>For each rational number <span>(p/qin (1/2,sqrt{2}/2))</span> one can construct an <span>(mathbb {S}^1)</span>-equivariant minimal torus in <span>(mathbb {S}^3)</span> called Otsuki torus and denoted by <span>(O_{p/q})</span>. The Lawson’s bipolar surface construction applied to <span>(O_{p/q})</span> gives a minimal torus <span>(widetilde{O}_{p/q})</span> in <span>(mathbb {S}^4)</span>. In this paper we give upper and lower bounds on the Morse index and the nullity of these tori for <i>p</i>/<i>q</i> close to <span>(sqrt{2}/2)</span>. We also state a numerically assisted conjecture concerning the general case.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"27 4","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142600583","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
Sharp Interface Limit for a Quasi-linear Large Deviation Rate Function 准线性大偏差率函数的锐界面极限
IF 0.9 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2024-10-16 DOI: 10.1007/s11040-024-09491-y
Takashi Kagaya, Kenkichi Tsunoda
{"title":"Sharp Interface Limit for a Quasi-linear Large Deviation Rate Function","authors":"Takashi Kagaya,&nbsp;Kenkichi Tsunoda","doi":"10.1007/s11040-024-09491-y","DOIUrl":"10.1007/s11040-024-09491-y","url":null,"abstract":"<div><p>We discuss the sharp interface limit, leading to a mean curvature flow energy, for the rate function of the large deviation principle of a Glauber+Kawasaki process with speed change. We provide an explicit formula of the limiting functional given by the mobility and the transport coefficient.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"27 4","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142443364","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
KdV and mKdV Hierarchies and Schur Q-functions KdV 和 mKdV 层次和舒尔 Q 函数
IF 0.9 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2024-10-12 DOI: 10.1007/s11040-024-09493-w
Sumitaka Tabata
{"title":"KdV and mKdV Hierarchies and Schur Q-functions","authors":"Sumitaka Tabata","doi":"10.1007/s11040-024-09493-w","DOIUrl":"10.1007/s11040-024-09493-w","url":null,"abstract":"<div><p>We prove two conjectures on the Korteweg-de Vries (KdV) and modified KdV (mKdV) hierarchies and Schur Q-functions presented by Yamada. The first one is that the functions defined by Sato and Mori in 1980 coincide with Schur Q-functions indexed by even or odd strict partitions. Mizukawa, Nakajima, and Yamada gave an expression for this function using symmetric functions and Littlewood-Richardson coefficients. We prove that this expression coincides with the Schur Q-function by using the formula of Lascoux, Leclerc, and Thibon. The second one is that Schur Q-functions indexed by strict partitions which have odd parts form a basis for the space of Hirota polynomials of the KdV hierarchy, and that Schur Q-functions indexed by strict partitions which have even parts form a basis for the space of Hirota polynomials of the mKdV hierarchy. This conjecture is verified by rewriting the generating series of the KdV and mKdV hierarchies using the techniques of symmetric functions.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"27 4","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142431009","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
On Real Hyperelliptic Solutions of Focusing Modified KdV Equation 论聚焦修正 KdV 方程的实超椭圆解
IF 0.9 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2024-09-30 DOI: 10.1007/s11040-024-09490-z
Shigeki Matsutani
{"title":"On Real Hyperelliptic Solutions of Focusing Modified KdV Equation","authors":"Shigeki Matsutani","doi":"10.1007/s11040-024-09490-z","DOIUrl":"10.1007/s11040-024-09490-z","url":null,"abstract":"<div><p>We study the real hyperelliptic solutions of the focusing modified KdV (MKdV) equation of genus three. Since the complex hyperelliptic solutions of the focusing MKdV equation over <span>({{mathbb {C}}})</span> are associated with the real gauged MKdV equation, we present a novel construction related to the real hyperelliptic solutions of the gauged MKdV equation. When the gauge field is constant, it can be regarded as the real solution of the focusing MKdV equation, and thus we also discuss the behavior of the gauge field numerically.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"27 4","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142415134","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
Integrable System on Minimal Nilpotent Orbit 最小无势轨道上的可积分系统
IF 0.9 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2024-09-24 DOI: 10.1007/s11040-024-09489-6
Xinyue Tu
{"title":"Integrable System on Minimal Nilpotent Orbit","authors":"Xinyue Tu","doi":"10.1007/s11040-024-09489-6","DOIUrl":"10.1007/s11040-024-09489-6","url":null,"abstract":"<div><p>We show that for every complex simple Lie algebra <span>(mathfrak {g})</span>, the equations of Schubert divisors on the flag variety <span>(G/B^-)</span> give a complete integrable system of the minimal nilpotent orbit <span>(mathcal {O}_{min })</span>. The approach is motivated by the integrable system on Coulomb branch as reported by Braverman (arXiv preprint arXiv:1604.03625, 2016).We give explicit computations of these Hamiltonian functions, using Chevalley basis and a so-called Heisenberg algebra basis. For classical Lie algebras we rediscover the lower order terms of the celebrated Gelfand-Zeitlin system. For exceptional types we computed the number of Hamiltonian functions associated to each vertex of Dynkin diagram. They should be regarded as analogs of Gelfand-Zeitlin functions on exceptional type Lie algebras.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"27 4","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142413488","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
Two-Term Asymptotics of the Exchange Energy of the Electron Gas on Symmetric Polytopes in the High-Density Limit 高密度极限对称多面体上电子气体交换能的两期渐近线
IF 0.9 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2024-09-16 DOI: 10.1007/s11040-024-09485-w
Thiago Carvalho Corso
{"title":"Two-Term Asymptotics of the Exchange Energy of the Electron Gas on Symmetric Polytopes in the High-Density Limit","authors":"Thiago Carvalho Corso","doi":"10.1007/s11040-024-09485-w","DOIUrl":"10.1007/s11040-024-09485-w","url":null,"abstract":"<div><p>We derive a two-term asymptotic expansion for the exchange energy of the free electron gas on strictly tessellating polytopes and fundamental domains of lattices in the thermodynamic limit. This expansion comprises a bulk (volume-dependent) term, the celebrated Dirac exchange, and a novel surface correction stemming from a boundary layer and finite-size effects. Furthermore, we derive analogous two-term asymptotic expansions for semi-local density functionals. By matching the coefficients of these asymptotic expansions, we obtain an integral constraint for semi-local approximations of the exchange energy used in density functional theory.\u0000</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"27 4","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-024-09485-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142266372","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
A Microlocal Investigation of Stochastic Partial Differential Equations for Spinors with an Application to the Thirring Model 旋子随机偏微分方程的微局部研究及对瑟林模型的应用
IF 0.9 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2024-08-28 DOI: 10.1007/s11040-024-09488-7
Alberto Bonicelli, Beatrice Costeri, Claudio Dappiaggi, Paolo Rinaldi
{"title":"A Microlocal Investigation of Stochastic Partial Differential Equations for Spinors with an Application to the Thirring Model","authors":"Alberto Bonicelli,&nbsp;Beatrice Costeri,&nbsp;Claudio Dappiaggi,&nbsp;Paolo Rinaldi","doi":"10.1007/s11040-024-09488-7","DOIUrl":"10.1007/s11040-024-09488-7","url":null,"abstract":"<div><p>On a <i>d</i>-dimensional Riemannian, spin manifold (<i>M</i>, <i>g</i>) we consider non-linear, stochastic partial differential equations for spinor fields, driven by a Dirac operator and coupled to an additive Gaussian, vector-valued white noise. We extend to the case in hand a procedure, introduced in Dappiaggi et al (Commun Contemp Math 27(07):2150075, 2022), for the scalar counterpart, which allows to compute at a perturbative level the expectation value of the solutions as well as the associated correlation functions accounting intrinsically for the underlying renormalization freedoms. This framework relies strongly on tools proper of microlocal analysis and it is inspired by the algebraic approach to quantum field theory. As a concrete example we apply it to a stochastic version of the Thirring model proving in particular that it lies in the subcritical regime if <span>(dle 2)</span>.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"27 3","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-024-09488-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201173","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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