On the foundation of equilibrium quantum statistical mechanics

TL;DR

This paper explores the foundational conditions for equilibrium quantum statistical mechanics, linking quantum distributions to classical ergodic systems through recent insights into chaotic dynamics.

Contribution

It establishes the ergodicity parameter as a key criterion for deriving quantum statistical distributions from classical ergodic Hamiltonian systems.

Findings

Ergodicity parameter determines validity of quantum statistical mechanics

Quantum distributions linked to classical chaotic motion

Conditions for quantum equilibrium derived from classical ergodicity

Abstract

We discuss the condition for the validity of equilibrium quantum statistical mechanics in the light of recent developments in the understanding of classical and quantum chaotic motion. In particular, the ergodicity parameter is shown to provide the conditions under which quantum statistical distributions can be derived from the quantum dynamics of a classical ergodic Hamiltonian system.