# Equilibration time scales in closed many-body quantum systems

## TL;DR

This paper demonstrates that dephasing is the key mechanism for equilibration in closed quantum systems and shows that local Hamiltonians lead to system-size-independent equilibration times, contrasting with previous bounds.

## Contribution

It identifies the energy scales governing equilibration times and proves that local Hamiltonians have banded matrix representations, resulting in realistic, non-negligible equilibration times.

## Key findings

- Dephasing is the main mechanism for quantum system equilibration.
- Local Hamiltonians have banded matrix representations in the energy basis.
- Equilibration times do not necessarily grow with system size for realistic systems.

## Abstract

We show that the physical mechanism for the equilibration of closed quantum systems is dephasing, and identify the energy scales that determine the equilibration timescale of a given observable. For realistic physical systems (e.g those with local Hamiltonians), our arguments imply timescales that do not increase with the system size, in contrast to previously known upper bounds. In particular we show that, for such Hamiltonians, the matrix representation of local observables in the energy basis is banded, and that this property is crucial in order to derive equilibration times that are non-negligible in macroscopic systems. Finally, we give an intuitive interpretation to recent theorems on equilibration time-scale.