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Gaussian fluctuations in the Equipartition Principle for Wigner matrices (2301.05181v2)
Published 12 Jan 2023 in math-ph, math.MP, and math.PR
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.