Geodesic
Gaussian fluctuations in the equipartition principle for Wigner matrices
Forum of Mathematics, Sigma, Tome 11 (2023)

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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. 
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     author = {Giorgio Cipolloni and L\'aszl\'o Erd\H{o}s and Joscha Henheik and Oleksii Kolupaiev},
     title = {Gaussian fluctuations in the equipartition principle for {Wigner} matrices},
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Giorgio Cipolloni; László Erdős; Joscha Henheik; Oleksii Kolupaiev. Gaussian fluctuations in the equipartition principle for Wigner matrices. Forum of Mathematics, Sigma, Tome 11 (2023). doi: 10.1017/fms.2023.70

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