Does Quantum Chaos Explain Quantum Statistical Mechanics?

Abstract

If a many-body quantum system approaches thermal equilibrium from a generic initial state, then the expectation value $\langleψ(t)|A_i|ψ(t)\rangle$, where $|ψ(t)\rangle$ is the system's state vector and $A_i$ is an experimentally accessible observable, should approach a constant value which is independent of the initial state, and equal to a thermal average of $A_i$ at an appropriate temperature. We show that this is the case for all simple observables whenever the system is classically chaotic.