Communications in Mathematical Physics最新文献_第9页

Nonlinear Anderson Localized States at Arbitrary Disorder 任意无序状态下的非线性安德森局部状态

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2024-10-24 DOI: 10.1007/s00220-024-05150-z

Wencai Liu, W.-M. Wang

引用次数: 0

WKB Asymptotics of Stokes Matrices, Spectral Curves and Rhombus Inequalities 斯托克斯矩阵、频谱曲线和菱形不等式的 WKB 渐进性

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2024-10-24 DOI: 10.1007/s00220-024-05133-0

Anton Alekseev, Andrew Neitzke, Xiaomeng Xu, Yan Zhou

{"title":"WKB Asymptotics of Stokes Matrices, Spectral Curves and Rhombus Inequalities","authors":"Anton Alekseev, Andrew Neitzke, Xiaomeng Xu, Yan Zhou","doi":"10.1007/s00220-024-05133-0","DOIUrl":"10.1007/s00220-024-05133-0","url":null,"abstract":"<div>We consider (ntimes n) systems of linear ODEs on (mathbb {P}^1) with a regular singularity at (z=0) and an irregular singularity of rank 1 (double pole) at (z=infty ). The monodromy data of such a system are described by upper and lower triangular Stokes matrices (S_pm ). We impose reality conditions which imply (S_-=S_+^dagger ). We study the leading WKB exponents of the Stokes matrices in parametrizations given by generalized minors and by spectral coordinates. We show that in a certain degeneration limit, called the caterpillar limit, the real parts of these exponents are given by periods of 1-cycles on a degenerate spectral curve. We then consider moving away from the caterpillar limit. Using exact WKB and spectral networks, we give predictions for asymptotics of generalized minors in terms of regularized periods on the spectral curve, in the cases (n = 2) and (n = 3). For (n=2) we verify directly that the predictions are correct, while for (n=3) they are new conjectures. Boalch’s theorem from Poisson geometry implies that the real parts of leading WKB exponents satisfy the rhombus (or interlacing) inequalities. We show for (n=2) and (n=3) that these inequalities are equivalent to the positivity of certain periods, and that this positivity is a consequence of the existence of certain finite webs. We also discuss the relation of the spectral networks with the cluster structures on dual Poisson–Lie groups considered by Goncharov–Shen, and with certain ({{mathcal {N}}}=2) supersymmetric quantum field theories in dimension four. In the field theory context the caterpillar limit becomes a weak-coupling limit, and the finite webs are interpreted as BPS particles.\u0000</div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"405 11","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-024-05133-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142518887","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

B-brane Transport and Grade Restriction Rule for Determinantal Varieties 确定性变种的 B-膜传输和等级限制规则

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2024-10-23 DOI: 10.1007/s00220-024-05153-w

Ban Lin, Mauricio Romo

引用次数: 0

Asymptotic Stability in the Critical Space of 2D Monotone Shear Flow in the Viscous Fluid 粘性流体中二维单调剪切流临界空间的渐近稳定性

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2024-10-16 DOI: 10.1007/s00220-024-05155-8

Hui Li, Weiren Zhao

{"title":"Asymptotic Stability in the Critical Space of 2D Monotone Shear Flow in the Viscous Fluid","authors":"Hui Li, Weiren Zhao","doi":"10.1007/s00220-024-05155-8","DOIUrl":"10.1007/s00220-024-05155-8","url":null,"abstract":"<div>In this paper, we study the long-time behavior of the solutions to the two-dimensional incompressible free Navier Stokes equation (without forcing) with small viscosity (nu ), when the initial data is close to stable monotone shear flows. We prove the asymptotic stability and obtain the sharp stability threshold (nu ^{frac{1}{2}}) for perturbations in the critical space (H^{log}_xL^2_y). Specifically, if the initial velocity (V_{in}) and the corresponding vorticity (W_{in}) are (nu ^{frac{1}{2}})-close to the shear flow ((b_{in}(y),0)) in the critical space, i.e., (Vert V_{in}-(b_{in}(y),0)Vert _{L_{x,y}^2}+Vert W_{in}-(-partial _yb_{in})Vert _{H^{log}_xL^2_y}le varepsilon nu ^{frac{1}{2}}), then the velocity V(t) stay (nu ^{frac{1}{2}})-close to a shear flow (b(t, y), 0) that solves the free heat equation ((partial _t-nu partial _{yy})b(t,y)=0). We also prove the enhanced dissipation and inviscid damping, namely, the nonzero modes of vorticity and velocity decay in the following sense (Vert W_{ne }Vert _{L^2}lesssim varepsilon nu ^{frac{1}{2}}e^{-cnu ^{frac{1}{3}}t}) and (Vert V_{ne }Vert _{L^2_tL^2_{x,y}}lesssim varepsilon nu ^{frac{1}{2}}). In the proof, we construct a time-dependent wave operator corresponding to the Rayleigh operator (b(t,y)textrm{Id}-partial _{yy}b(t,y)Delta ^{-1}), which could be useful in future studies.</div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"405 11","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142443253","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The Spin-Statistics Theorem for Topological Quantum Field Theories 拓扑量子场论的自旋统计定理

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2024-10-12 DOI: 10.1007/s00220-024-05140-1

Luuk Stehouwer

引用次数: 0

Reducibility Without KAM 无 KAM 的可再现性

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2024-10-12 DOI: 10.1007/s00220-024-05105-4

F. Argentieri, B. Fayad

引用次数: 0

Nonlinear Dynamics for the Ising Model 伊辛模型的非线性动力学

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2024-10-12 DOI: 10.1007/s00220-024-05129-w

Pietro Caputo, Alistair Sinclair

{"title":"Nonlinear Dynamics for the Ising Model","authors":"Pietro Caputo, Alistair Sinclair","doi":"10.1007/s00220-024-05129-w","DOIUrl":"10.1007/s00220-024-05129-w","url":null,"abstract":"<div>We introduce and analyze a natural class of nonlinear dynamics for spin systems such as the Ising model. This class of dynamics is based on the framework of mass action kinetics, which models the evolution of systems of entities under pairwise interactions, and captures a number of important nonlinear models from various fields, including chemical reaction networks, Boltzmann’s model of an ideal gas, recombination in population genetics and genetic algorithms. In the context of spin systems, it is a natural generalization of linear dynamics based on Markov chains, such as Glauber dynamics and block dynamics, which are by now well understood. However, the inherent nonlinearity makes the dynamics much harder to analyze, and rigorous quantitative results so far are limited to processes which converge to essentially trivial stationary distributions that are product measures. In this paper we provide the first quantitative convergence analysis for natural nonlinear dynamics in a combinatorial setting where the stationary distribution contains non-trivial correlations, namely spin systems at high temperatures. We prove that nonlinear versions of both the Glauber dynamics and the block dynamics converge to the Gibbs distribution of the Ising model (with given external fields) in times (O(nlog n)) and (O(log n)) respectively, where n is the size of the underlying graph (number of spins). Given the lack of general analytical methods for such nonlinear systems, our analysis is unconventional, and combines tools such as information percolation (due in the linear setting to Lubetzky and Sly), a novel coupling of the Ising model with Erdős-Rényi random graphs, and non-traditional branching processes augmented by a “fragmentation” process. Our results extend immediately to any spin system with a finite number of spins and bounded interactions.</div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"405 11","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-024-05129-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142431059","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Onsager–Machlup Functional for (text {SLE}_{kappa }) Loop Measures Onsager-Machlup 函数用于（text {SLE}_{kappa }) 循环措施

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2024-10-12 DOI: 10.1007/s00220-024-05071-x

Marco Carfagnini, Yilin Wang

引用次数: 0

Coloured Invariants of Torus Knots, Algebras, and Relative Asymptotic Weight Multiplicities 环结、代数和相对渐近权乘的彩色不变式

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2024-10-12 DOI: 10.1007/s00220-024-05130-3

Shashank Kanade

引用次数: 0

Levin-Wen is a Gauge Theory: Entanglement from Topology 列文-温是一种量子理论来自拓扑学的纠缠