Tags → #eigenstate thermalization

Eigenstate thermalization hypothesis for Wigner matrices
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, rigorously verifying the Eigenstate Thermalization Hypothesis.

Normal fluctuation in quantum ergodicity for Wigner matrices
We prove a CLT for quadratic forms of eigenvectors of Wigner matrices with arbitrary deterministic matrices, considerably strengthening previous results on quantum unique ergodicity.

Optimal Lower Bound on Eigenvector Overlaps for nonHermitian Random Matrices
We show that already a small noise completely thermalizes the bulk singular vectors of arbitrary deterministic matrices. In particular we prove a strong form of Quantum Unique Ergodicity (QUE) with an optimal speed of convergence for such matrices.