Gaussian fluctuations in the Equipartition Principle for Wigner matrices
Mathematical Physics
2023-12-21 v2 math.MP
Probability
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.
Keywords
Cite
@article{arxiv.2301.05181,
title = {Gaussian fluctuations in the Equipartition Principle for Wigner matrices},
author = {Giorgio Cipolloni and László Erdős and Joscha Henheik and Oleksii Kolupaiev},
journal= {arXiv preprint arXiv:2301.05181},
year = {2023}
}
Comments
34 pages, 1 figure; final version