arXiv - PHYS - Exactly Solvable and Integrable Systems最新文献_第7页

Gauge equivalence of 1+1 Calogero-Moser-Sutherland field theory and higher rank trigonometric Landau-Lifshitz model 1+1 卡洛吉罗-莫瑟-萨瑟兰场论与高阶三角兰道-利夫希茨模型的等价性

arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-03-01 DOI: arxiv-2403.00428

K. Atalikov, A. Zotov

引用次数: 0

New cluster algebras from old: integrability beyond Zamolodchikov periodicity 新簇代数源于旧簇代数：超越扎莫洛奇科夫周期性的可整性

arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-03-01 DOI: arxiv-2403.00721

Andrew N. W. Hone, Wookyung Kim, Takafumi Mase

{"title":"New cluster algebras from old: integrability beyond Zamolodchikov periodicity","authors":"Andrew N. W. Hone, Wookyung Kim, Takafumi Mase","doi":"arxiv-2403.00721","DOIUrl":"https://doi.org/arxiv-2403.00721","url":null,"abstract":"We consider discrete dynamical systems obtained as deformations of mutations\u0000in cluster algebras associated with finite-dimensional simple Lie algebras. The\u0000original (undeformed) dynamical systems provide the simplest examples of\u0000Zamolodchikov periodicity: they are affine birational maps for which every\u0000orbit is periodic with the same period. Following on from preliminary work by\u0000one of us with Kouloukas, here we present integrable maps obtained from\u0000deformations of cluster mutations related to the following simple root systems:\u0000$A_3$, $B_2$, $B_3$ and $D_4$. We further show how new cluster algebras arise,\u0000by considering Laurentification, that is, a lifting to a higher-dimensional map\u0000expressed in a set of new variables (tau functions), for which the dynamics\u0000exhibits the Laurent property. For the integrable map obtained by deformation\u0000of type $A_3$, which already appeared in our previous work, we show that there\u0000is a commuting map of Quispel-Roberts-Thompson (QRT) type which is built from a\u0000composition of mutations and a permutation applied to the same cluster algebra\u0000of rank 6, with an additional 2 frozen variables. Furthermore, both the\u0000deformed $A_3$ map and the QRT map correspond to addition of a point in the\u0000Mordell-Weil group of a rational elliptic surface of rank two, and the\u0000underlying cluster algebra comes from a quiver that mutation equivalent to the\u0000$q$-Painlev'e III quiver found by Okubo. The deformed integrable maps of types\u0000$B_2$, $B_3$ and $D_4$ are also related to elliptic surfaces.","PeriodicalId":501592,"journal":{"name":"arXiv - PHYS - Exactly Solvable and Integrable Systems","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140035711","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The Shigesada-Kawasaki-Teramoto model: conditional symmetries, exact solutions and their properties 重砂田-川崎-寺本模型：条件对称性、精确解及其特性

arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-02-29 DOI: arxiv-2402.19050

Roman Cherniha, Vasyl' Davydovych, John R. King

引用次数: 0

Solitary cluster waves in periodic potentials: Formation, propagation, and soliton-mediated particle transport 周期势中的孤簇波：形成、传播和孤子介导的粒子传输

arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-02-27 DOI: arxiv-2402.17469

Alexander P. Antonov, Artem Ryabov, Philipp Maass

{"title":"Solitary cluster waves in periodic potentials: Formation, propagation, and soliton-mediated particle transport","authors":"Alexander P. Antonov, Artem Ryabov, Philipp Maass","doi":"arxiv-2402.17469","DOIUrl":"https://doi.org/arxiv-2402.17469","url":null,"abstract":"Transport processes in crowded periodic structures are often mediated by\u0000cooperative movements of particles forming clusters. Recent theoretical and\u0000experimental studies of driven Brownian motion of hard spheres showed that\u0000cluster-mediated transport in one-dimensional periodic potentials can proceed\u0000in form of solitary waves. We here give a comprehensive description of these\u0000solitons. Fundamental for our analysis is a static presoliton state, which is\u0000formed by a periodic arrangements of basic stable clusters. Their size follows\u0000from a geometric principle of minimum free space. Adding one particle to the\u0000presoliton state gives rise to solitons. We derive the minimal number of\u0000particles needed for soliton formation, number of solitons at larger particle\u0000numbers, soliton velocities and soliton-mediated particle currents. Incomplete\u0000relaxations of the basic clusters are responsible for an effective repulsive\u0000soliton-soliton interaction seen in measurements. Our results provide a\u0000theoretical basis for describing experiments on cluster-mediated particle\u0000transport in periodic potentials.","PeriodicalId":501592,"journal":{"name":"arXiv - PHYS - Exactly Solvable and Integrable Systems","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140009099","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Nonlocal Symmetries of Two 2-component Equations of Camassa-Holm Type 卡马萨-霍尔姆式两分式方程的非局部对称性

arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-02-20 DOI: arxiv-2402.12618

Ziqi Li, Kai Tian

引用次数: 0

Non-local time evolution equation with singular integral and its application to traffic flow model 带奇异积分的非局部时间演化方程及其在交通流模型中的应用

arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-02-20 DOI: arxiv-2402.13128

Kohei Higashi

引用次数: 0

The Volterra lattice, Abel's equation of the first kind, and the SIR epidemic models 沃尔特拉晶格、阿贝尔第一类方程和 SIR 流行病模型

arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-02-19 DOI: arxiv-2402.11888

Atsushi Nobe

引用次数: 0

Gauge-Independent Metric Reconstruction of Perturbations of Vacuum Spherically-Symmetric Spacetimes 与量纲无关的真空球对称时空扰动的度量重构

arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-02-15 DOI: arxiv-2402.10004

Michele Lenzi, Carlos F. Sopuerta

{"title":"Gauge-Independent Metric Reconstruction of Perturbations of Vacuum Spherically-Symmetric Spacetimes","authors":"Michele Lenzi, Carlos F. Sopuerta","doi":"arxiv-2402.10004","DOIUrl":"https://doi.org/arxiv-2402.10004","url":null,"abstract":"Perturbation theory of vacuum spherically-symmetric spacetimes (including the\u0000cosmological constant) has greatly contributed to the understanding of black\u0000holes, relativistic compact stars and even inhomogeneous cosmological models.\u0000The perturbative equations can be decoupled in terms of (gauge-invariant)\u0000master functions satisfying $1+1$ wave equations. In this work, building on\u0000previous work on the structure of the space of master functions and equations,\u0000we study the reconstruction of the metric perturbations in terms of the master\u0000functions. To that end, we consider the general situation in which the\u0000perturbations are driven by an arbitrary energy-momentum tensor. Then, we\u0000perform the metric reconstruction in a completely general perturbative gauge.\u0000In doing so, we investigate the role of Darboux transformations and Darboux\u0000covariance, responsible for the isospectrality between odd and even parity in\u0000the absence of matter sources and also of the physical equivalence between the\u0000descriptions based on all the possible master equations. We also show that the\u0000metric reconstruction can be carried out in terms of any of the possible master\u0000functions and that the expressions admit an explicitly covariant form.","PeriodicalId":501592,"journal":{"name":"arXiv - PHYS - Exactly Solvable and Integrable Systems","volume":"34 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139772718","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Davydov's soliton in an external alternating magnetic field 外交变磁场中的达维多夫孤子

arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-02-14 DOI: arxiv-2402.09172

Larissa Brizhik

引用次数: 0

Symplectic mechanics of relativistic spinning compact bodies II.: Canonical formalism in the Schwarzschild spacetime 相对论旋转紧凑体的交映力学 II：施瓦兹柴尔德时空中的经典形式主义

arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-02-07 DOI: arxiv-2402.05049

Paul Ramond, Soichiro Isoyama

{"title":"Symplectic mechanics of relativistic spinning compact bodies II.: Canonical formalism in the Schwarzschild spacetime","authors":"Paul Ramond, Soichiro Isoyama","doi":"arxiv-2402.05049","DOIUrl":"https://doi.org/arxiv-2402.05049","url":null,"abstract":"This work is the second part in a series aiming at exploiting tools from\u0000Hamiltonian mechanics to study the motion of an extended body in general\u0000relativity. In the first part of this work, we constructed a 10-dimensional,\u0000covariant Hamiltonian framework that encodes all the linear-in-spin corrections\u0000to the geodesic motion. This formulation, although non-canonical, revealed\u0000that, at this linear-in-spin order, the integrability of Schwarzschild and Kerr\u0000geodesics remain. Building on this formalism, in the present work, we translate\u0000this abstract integrability result into tangible applications for\u0000linear-in-spin dynamics of a compact object into a Schwarzschild background\u0000spacetime. In particular, we construct a canonical system of coordinates which\u0000exploits the spherical symmetry of the Schwarzschild spacetime. They are based\u0000on a relativistic generalization of the classical Andoyer variables of\u0000Newtonian rigid body motion. This canonical setup, then, allows us to derive\u0000ready-to-use formulae for action-angle coordinates and gauge-invariant\u0000Hamiltonian frequencies, which automatically include all linear-in-spin\u0000effects. No external parameters or ad hoc choices are necessary, and the\u0000framework can be used to find complete solutions by quadrature of generic,\u0000bound, linear-in-spin orbits, including orbital inclination, precession and\u0000eccentricity, as well as spin precession. We demonstrate the strength of the\u0000formalism in the simple setting of circular orbits with arbitrary spin and\u0000orbital precession, and validate them against known results in the literature.","PeriodicalId":501592,"journal":{"name":"arXiv - PHYS - Exactly Solvable and Integrable Systems","volume":"74 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139760314","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0