Thermalisation for Wigner matrices
نویسندگان
چکیده
We compute the deterministic approximation of products Sobolev functions large Wigner matrices $W$ and provide an optimal error bound on their fluctuation with very high probability. This generalizes Voiculescu's seminal theorem [Voiculescu 1991] from polynomials to general functions, as well tracial quantities individual matrix elements. Applying result $\exp(\mathrm{i} tW)$ for $t$, we obtain a precise decay rate overlaps several temporally separated Heisenberg time evolutions; thus demonstrate thermalisation effect unitary group generated by matrices.
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2022
ISSN: ['0022-1236', '1096-0783']
DOI: https://doi.org/10.1016/j.jfa.2022.109394