Mathematical Physics Seminar, Tue, Oct 12, 4:30pm Jadwin A-06, Giorgio Cipolloni, PCTS, "Extension of Wigner's Vision to Quantum Chaos"

Tue, Oct 12, 2021, 4:30 pm
Jadwin A-06

After reviewing recent progress in random Hermitian and non-Hermitian matrix theory, we prove that eigenvectors of Wigner matrices satisfy the Eigenstate Thermalisation Hypothesis (ETH), which is a strong form of Quantum Unique ergodicity (QUE) with optimal speed of convergence. This requires proving certain multi-resolvent local laws established via a novel bootstrap scheme. Additionally, we also prove that the fluctuations in QUE are universal, relying on energy methods for multi-particle Dyson Brownian motion.