维格纳型矩阵的特征态热化假说

IF 2.2 1区物理与天体物理 Q1 PHYSICS, MATHEMATICAL

Communications in Mathematical Physics Pub Date : 2024-11-06 DOI:10.1007/s00220-024-05143-y

László Erdős, Volodymyr Riabov

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引用次数: 0

摘要

我们证明了自洽谱主体中一般维格纳型矩阵的特征态热化假说，并对任意阶观测值的波动进行了最优控制。作为主要的技术要素，我们证明了具有规则观测值的 Wigner 型矩阵的一个和两个解析子的秩均匀最优局部律。我们的结果在方差轮廓的一般条件下成立，甚至允许许多消失的条目，证明了特征态热化在不同类别的随机矩阵集合中稳健地发生，对于这些随机矩阵集合，底层量子系统具有非三维空间结构。

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Eigenstate Thermalization Hypothesis for Wigner-Type Matrices

We prove the Eigenstate Thermalization Hypothesis for general Wigner-type matrices in the bulk of the self-consistent spectrum, with optimal control on the fluctuations for obs ervables of arbitrary rank. As the main technical ingredient, we prove rank-uniform optimal local laws for one and two resolvents of a Wigner-type matrix with regular observables. Our results hold under very general conditions on the variance profile, even allowing many vanishing entries, demonstrating that Eigenstate Thermalization occurs robustly across a diverse class of random matrix ensembles, for which the underlying quantum system has a non-trivial spatial structure.

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来源期刊

Communications in Mathematical Physics 物理-物理：数学物理

CiteScore

4.70

自引率

8.30%

发文量

226

审稿时长

3-6 weeks

期刊介绍： The mission of Communications in Mathematical Physics is to offer a high forum for works which are motivated by the vision and the challenges of modern physics and which at the same time meet the highest mathematical standards.