Statistical structural properties of many-body chaotic eigenfunctions and applications

TL;DR

This paper develops a semiperturbative approach to analyze the statistical structural properties of many-body quantum chaotic eigenfunctions, providing insights into eigenstate structure, reduced density matrices, and the eigenstate thermalization hypothesis.

Contribution

It introduces a novel semiperturbative theoretical framework for characterizing eigenfunction properties in many-body quantum chaos, supported by numerical validation.

Findings

Derived average shape and fluctuations of eigenfunctions

Analyzed reduced density matrix properties in eigenstates

Explored structure of off-diagonal functions in ETH framework

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.