Statistical Mechanics From Unitary Dynamics

Abstract

In this thesis I present a derivation of statistical mechanics starting from a closed, isolated quantum many body system. I first establish under what conditions we expect static equilibrium to emerge. It is found that the purity of the diagonal ensemble is a sufficient criteria for equilibration to occur and avoid short time recurrences. I next derive the usual ensembles of statistical mechanics using the principle of maximum entropy. These ensembles are then connected to the diagonal ensemble through the strong and the weak eigenstate thermalization hypothesis (ETH). Counter examples to ETH are discussed along with the process of scrambling. The thesis contains three contributed articles relevant to this introductory chapter studying early time relaxation, recurrences and scrambling.