Statistical structural properties of many-body chaotic eigenfunctions and applications

Wen-ge Wang; Qingchen Li; Jiaozi Wang; Xiao Wang

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arXiv · 2512.07016

Statistical structural properties of many-body chaotic eigenfunctions and applications

Wen-ge Wang·Qingchen Li·Jiaozi Wang·Xiao Wang

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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.

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Wen-ge Wang, Qingchen Li, Jiaozi Wang, Xiao Wang. 2025-12-07. Statistical structural properties of many-body chaotic eigenfunctions and applications. https://arxiv.org/abs/2512.07016

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