Statistical structural properties of many-body chaotic eigenfunctions and applications
Abstract
In this paper, we employ a semiperturbative theory to study the statistical structural properties of energy eigenfunctions (EFs) in many-body quantum chaotic systems consisting of a central system coupled to an environment. Under certain assumptions, we derive both the average shape and the statistical fluctuations of EFs on the basis formed by the direct product of the energy eigenbases of the system and the environment. Furthermore, we apply our results to two fundamental questions: (i) the properties of the reduced density matrix of the central system in an eigenstate, and (ii) the structure of the off-diagonal smooth function within the framework of the eigenstate thermalization hypothesis. Numerical results are also presented in support of our main findings.
Cite
@article{arxiv.2512.07016,
title = {Statistical structural properties of many-body chaotic eigenfunctions and applications},
author = {Wen-ge Wang and Qingchen Li and Jiaozi Wang and Xiao Wang},
journal= {arXiv preprint arXiv:2512.07016},
year = {2025}
}
Comments
22 pages, 3 figures