Gaussian fluctuations in the Equipartition Principle for Wigner matrices

TL;DR

This paper investigates the quantum fluctuations around the equipartition principle in disordered quantum systems modeled by Wigner matrices, establishing Gaussian fluctuation behavior and the Eigenstate Thermalisation Hypothesis for such systems.

Contribution

It proves the Eigenstate Thermalisation Hypothesis and Gaussian fluctuations for quadratic forms of Wigner matrix eigenvectors with arbitrary deformation, advancing understanding of quantum chaos.

Findings

Proves Gaussian fluctuation for quadratic forms of Wigner eigenvectors.

Establishes the Eigenstate Thermalisation Hypothesis in this context.

Analyzes energy distribution in disordered quantum systems.

Abstract

The total energy of an eigenstate in a composite quantum system tends to be distributed equally among its constituents. We identify the quantum fluctuation around this equipartition principle in the simplest disordered quantum system consisting of linear combinations of Wigner matrices. As our main ingredient, we prove the Eigenstate Thermalisation Hypothesis and Gaussian fluctuation for general quadratic forms of the bulk eigenvectors of Wigner matrices with an arbitrary deformation.