Quantum Unique Ergodicity and its fluctuations for Wigner matrices

Giorgio Cipolloni

20-06-2023 - 14:00
Largo San Leonardo Murialdo,1 - Pal.C - Aula 211


We prove that the eigenvectors of Wigner matrices satisfy the Eigenstate Thermalization Hypothesis (ETH), which is a strong form of Quantum Unique Ergodicity (QUE) with optimal speed of convergence.
Then, using this a priori bound as an input, we analyze the Stochastic Eigenstate Equation (SEE) and prove a Wigner matrix analog of the Berry random wave conjecture.
org: CAPUTO Pietro