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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