arXiv - PHYS - Exactly Solvable and Integrable Systems最新文献_第2页

Triple critical point and emerging temperature scales in $SU(N)$ ferromagnetism at large $N$ 大 N$ 时 SU(N)$ 铁磁性中的三临界点和新出现的温度尺度

arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-08-15 DOI: arxiv-2408.08357

Alexios P. Polychronakos, Konstantinos Sfetsos

{"title":"Triple critical point and emerging temperature scales in $SU(N)$ ferromagnetism at large $N$","authors":"Alexios P. Polychronakos, Konstantinos Sfetsos","doi":"arxiv-2408.08357","DOIUrl":"https://doi.org/arxiv-2408.08357","url":null,"abstract":"The non-Abelian ferromagnet recently introduced by the authors, consisting of\u0000atoms in the fundamental representation of $SU(N)$, is studied in the limit\u0000where $N$ becomes large and scales as the square root of the number of atoms\u0000$n$. This model exhibits additional phases, as well as two different\u0000temperature scales related by a factor $N!/!ln N$. The paramagnetic phase\u0000splits into a \"dense\" and a \"dilute\" phase, separated by a third-order\u0000transition and leading to a triple critical point in the scale parameter\u0000$n/N^2$ and the temperature, while the ferromagnetic phase exhibits additional\u0000structure, and a new paramagnetic-ferromagnetic metastable phase appears at the\u0000larger temperature scale. These phases can coexist, becoming stable or\u0000metastable as temperature varies. A generalized model in which the number of\u0000$SU(N)$-equivalent states enters the partition function with a nontrivial\u0000weight, relevant, e.g., when there is gauge invariance in the system, is also\u0000studied and shown to manifest similar phases, with the dense-dilute phase\u0000transition becoming second-order in the fully gauge invariant case.","PeriodicalId":501592,"journal":{"name":"arXiv - PHYS - Exactly Solvable and Integrable Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142194556","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

Integrable hierarchy for homogeneous realization of toroidal Lie algebra $mathcal{L}^{rm tor}_{r+1}(mathfrak{sl}_ell)$ 环形李代数$mathcal{L}^{rm tor}_{r+1}(mathfrak{sl}_ell)$ 的同质实现的可积分层次结构

arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-08-14 DOI: arxiv-2408.07376

Chao-Zhong Wu, Yi Yang

引用次数: 0

The massless S-matrix of integrable $σ$-models 可积分 $σ$ 模型的无质量 S 矩阵

arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-08-07 DOI: arxiv-2408.03673

George Georgiou

引用次数: 0

Generalised BBGKY hierarchy for near-integrable dynamics 近可积分动力学的广义 BBGKY 层次结构

arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-08-01 DOI: arxiv-2408.00593

Leonardo Biagetti, Maciej Lebek, Milosz Panfil, Jacopo De Nardis

{"title":"Generalised BBGKY hierarchy for near-integrable dynamics","authors":"Leonardo Biagetti, Maciej Lebek, Milosz Panfil, Jacopo De Nardis","doi":"arxiv-2408.00593","DOIUrl":"https://doi.org/arxiv-2408.00593","url":null,"abstract":"We consider quantum or classical many-body Hamiltonian systems, whose\u0000dynamics is given by an integrable, contact interactions, plus another,\u0000possibly long-range, generic two-body potential. We show how the dynamics of\u0000local observables is given in terms of a generalised version of\u0000Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy, which we denote as gBBGKY, which\u0000is built for the densities, and their correlations, of the quasiparticles of\u0000the underlying integrable model. Unlike the usual cases of perturbation theory\u0000from free gases, the presence of local interactions in the integrable model\u0000\"lifts\" the so-called kinetic blocking, and the second layer of the hierarchy\u0000reproduces the dynamics at all time-scales. The latter consists of a fast\u0000pre-equilibration to a non-thermal steady state, and its subsequent\u0000thermalisation to a Gibbs ensemble. We show how the final relaxation is encoded\u0000into a Boltzmann scattering integral involving three or higher\u0000body-scatterings, and which, remarkably, is entirely determined by the\u0000diffusion constants of the underlying integrable model. We check our results\u0000with exact molecular dynamics simulations, finding perfect agreement. Our\u0000results show how gBBGKY can be successfully employed in quantum systems to\u0000compute scattering integrals and Fermi's golden rule transition rates.","PeriodicalId":501592,"journal":{"name":"arXiv - PHYS - Exactly Solvable and Integrable Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141884009","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

Localized stem structures in quasi-resonant two-soliton solutions for the asymmetric Nizhnik-Novikov-Veselov system 不对称 Nizhnik-Novikov-Veselov 系统准共振双孑子解中的局部茎结构

arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-07-30 DOI: arxiv-2407.20875

Feng Yuan, Jiguang Rao, Jingsong He, Yi Cheng

{"title":"Localized stem structures in quasi-resonant two-soliton solutions for the asymmetric Nizhnik-Novikov-Veselov system","authors":"Feng Yuan, Jiguang Rao, Jingsong He, Yi Cheng","doi":"arxiv-2407.20875","DOIUrl":"https://doi.org/arxiv-2407.20875","url":null,"abstract":"Elastic collisions of solitons generally have a finite phase shift. When the\u0000phase shift has a finitely large value, the two vertices of the\u0000(2+1)-dimensional 2-soliton are significantly separated due to the phase shift,\u0000accompanied by the formation of a local structure connecting the two V-shaped\u0000solitons. We define this local structure as the stem structure. This study\u0000systematically investigates the localized stem structures between two solitons\u0000in the (2+1)-dimensional asymmetric Nizhnik-Novikov-Veselov system. These stem\u0000structures, arising from quasi-resonant collisions between the solitons,\u0000exhibit distinct features of spatial locality and temporal invariance. We\u0000explore two scenarios: one characterized by weakly quasi-resonant collisions\u0000(i.e. $a_{12}approx 0$), and the other by strongly quasi-resonant collisions\u0000(i.e. $a_{12}approx +infty$). Through mathematical analysis, we extract\u0000comprehensive insights into the trajectories, amplitudes, and velocities of the\u0000soliton arms. Furthermore, we discuss the characteristics of the stem\u0000structures, including their length and extreme points. Our findings shed new\u0000light on the interaction between solitons in the (2+1)-dimensional asymmetric\u0000Nizhnik-Novikov-Veselov system.","PeriodicalId":501592,"journal":{"name":"arXiv - PHYS - Exactly Solvable and Integrable Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141873405","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

Solvable nonlinear systems of 2 recursions displaying interesting evolutions 可解的非线性 2 个递推系统显示出有趣的演变

arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-07-20 DOI: arxiv-2407.18270

Francesco Calogero

引用次数: 0

Integrability in Perturbed Black Holes: Background Hidden Structures 扰动黑洞中的积分性：背景隐藏结构

arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-07-19 DOI: arxiv-2407.14196

José Luis Jaramillo, Michele Lenzi, Carlos F. Sopuerta

{"title":"Integrability in Perturbed Black Holes: Background Hidden Structures","authors":"José Luis Jaramillo, Michele Lenzi, Carlos F. Sopuerta","doi":"arxiv-2407.14196","DOIUrl":"https://doi.org/arxiv-2407.14196","url":null,"abstract":"In this work we investigate the presence of integrable hidden structures in\u0000the dynamics of perturbed non-rotating black holes (BHs). This can also be\u0000considered as a first step in a wider program of an effective identification of\u0000``slow'' and ``fast'' degrees of freedom (DoFs) in the (binary) BH dynamics,\u0000following a wave-mean flow perspective. The slow DoFs would be associated with\u0000a nonlinear integrable dynamics, on which the fast ones propagate following an\u0000effective linear dynamics. BH perturbation theory offers a natural ground to\u0000test these properties. Indeed, the decoupling of Einstein equations into wave\u0000master equations with a potential provides an instance of such splitting into\u0000(frozen) slow DoFs (background potential) over which the linear dynamics of the\u0000fast ones (perturbation master functions) evolve. It has been recently shown\u0000that these wave equations possess an infinite number of symmetries that\u0000correspond to the flow of the infinite hierarchy of Korteweg-de Vries (KdV)\u0000equations. Starting from these results, we systematically investigate the\u0000presence of integrable structures in BH perturbation theory. We first study\u0000them in Cauchy slices and then extend the analysis to hyperboloidal foliations.\u0000This second step introduces a splitting of the master equation into bulk and\u0000boundary contributions, unveiling an underlying structural relation with the\u0000slow and fast DoFs. This insight represents a first step to establish the\u0000integrable structures associated to the slow DoFs as bulk symmetries of the\u0000dynamics of perturbed BHs.","PeriodicalId":501592,"journal":{"name":"arXiv - PHYS - Exactly Solvable and Integrable Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141745634","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 integrable hierarchy and the nonlinear Riemann-Hilbert problem associated with one typical Einstein-Weyl physico-geometric dispersionless system 与一个典型的爱因斯坦-韦尔物理几何无分散系统相关的可积分层次结构和非线性黎曼-希尔伯特问题

arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-07-16 DOI: arxiv-2407.11515

Ge Yi, Tangna Lv, Kelei Tian, Ying Xu

引用次数: 0

R-matrix for the XX spin chain at the special imaginary value of staggered magnetic field 交错磁场特殊虚值下 XX 自旋链的 R 矩阵

arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-07-15 DOI: arxiv-2407.10395

P. N. Bibikov

引用次数: 0

The Volterra Integrable case. Novel analytical and numerical results 伏特拉积分情况。新颖的分析和数值结果

arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-07-12 DOI: arxiv-2407.09155

M. Scalia, O. Ragnisco, B. Tirozzi, F. Zullo

引用次数: 0