Generalization of von Neumann's Approach to Thermalization

TL;DR

This paper extends von Neumann's approach to demonstrate thermalization in isolated quantum many-body systems, showing that expectation values align with microcanonical averages for most late times without restrictive assumptions on observables.

Contribution

It generalizes von Neumann's method by removing assumptions about observable orientations, broadening the applicability to arbitrary initial states with well-defined energy.

Findings

Expectation values converge to microcanonical averages at late times.

Thermalization holds for most initial states with well-defined energy.

The approach does not require special orientations of observables or eigenvectors.

Abstract

Thermalization of isolated many-body systems is demonstrated by generalizing an approach originally due to von Neumann: For arbitrary initial states with a macroscopically well-defined energy, quantum mechanical expectation values become indistinguishable from the corresponding microcanonical expectation values for the overwhelming majority of all sufficiently late times. As in von Neumann's work, the eigenvectors of the Hamiltonian and of the considered observable are required to not exhibit any specially tailored (untypical) orientation relative to each other. But all of von Neumann's further assumptions about the admitted observables are abandoned.