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Updated: Dec 30, 2025

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

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Eigenstate Thermalization and Rotational Invariance in Ergodic Quantum Systems.

Laura Foini¹, Jorge Kurchan²

¹IPhT, CNRS, CEA, Université Paris Saclay, 91191 Gif-sur-Yvette, France.

Physical Review Letters

|January 18, 2020

Summary

This summary is machine-generated.

Generic matrix models and quantum systems exhibit a similar probability distribution for element differences. This study tests if this relation holds for non-localized quantum systems, offering a new test for the eigenstate thermalization hypothesis.

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Area of Science:

Quantum mechanics
Statistical physics
Condensed matter theory

Background:

Generic rotationally invariant matrix models show a specific probability distribution relation between diagonal and off-diagonal elements.
The eigenstate thermalization hypothesis (ETH) describes thermalization in quantum systems.

Purpose of the Study:

To test if the probability distribution relation observed in matrix models also holds for non-localized quantum systems with small energy differences.
To provide a stringent test for the eigenstate thermalization hypothesis beyond the standard Gaussian ensemble.

Main Methods:

Investigated the probability distribution of element differences in various quantum systems.
Applied the derived relation as a test for ETH.

Main Results:

The study confirms that the probability distribution relation holds in non-localized quantum systems.
This relation serves as a robust test for ETH in systems beyond the Gaussian ensemble.

Conclusions:

The findings extend the applicability of the observed probability distribution relation to a broader class of quantum systems.
The study validates the eigenstate thermalization hypothesis in diverse quantum models, including disordered spin chains, the Sachdev-Ye-Kitaev model, and Floquet systems.