TY - JOUR
AB - We prove that any deterministic matrix is approximately the identity in the eigenbasis of a large random Wigner matrix with very high probability and with an optimal error inversely proportional to the square root of the dimension. Our theorem thus rigorously verifies the Eigenstate Thermalisation Hypothesis by Deutsch (Phys Rev A 43:2046–2049, 1991) for the simplest chaotic quantum system, the Wigner ensemble. In mathematical terms, we prove the strong form of Quantum Unique Ergodicity (QUE) with an optimal convergence rate for all eigenvectors simultaneously, generalizing previous probabilistic QUE results in Bourgade and Yau (Commun Math Phys 350:231–278, 2017) and Bourgade et al. (Commun Pure Appl Math 73:1526–1596, 2020).
AU - Cipolloni, Giorgio
AU - Erdös, László
AU - Schröder, Dominik J
ID - 10221
IS - 2
JF - Communications in Mathematical Physics
SN - 0010-3616
TI - Eigenstate thermalization hypothesis for Wigner matrices
VL - 388
ER -