Eigenstate Thermalization Hypothesis

This lecture covers the Eigenstate Thermalization Hypothesis (ETH) in quantum systems, focusing on the random matrix theory and the behavior of observables in thermal equilibrium. The instructor explains how the ETH predicts the thermalization of quantum states and the statistical distribution of matrix elements. The lecture delves into the structure of matrix elements, the variance of observables, and the connection between ETH and out-of-time ordered correlators. The discussion also touches on the role of random matrices in modeling complex Hamiltonians and the implications of ETH for understanding quantum chaos.