Random product states at high temperature equilibrate exponentially well

TL;DR

This paper proves that for most local Hamiltonians, random product states at high temperature equilibrate rapidly with fluctuations that diminish exponentially with system size, demonstrating robust thermalization.

Contribution

It establishes that almost all local Hamiltonians exhibit exponential equilibration from high-temperature random product states, a significant advance in understanding quantum thermalization.

Findings

Expectation values equilibrate exponentially fast.

Fluctuations around stationary values are exponentially suppressed.

Results hold for almost all local Hamiltonians.

Abstract

We prove that for all but a measure zero set of local Hamiltonians, starting from random product states at sufficiently high but finite temperature, with overwhelming probability expectation values of observables equilibrate such that at sufficiently long times, fluctuations around the stationary value are exponentially small in the system size.