# Typical Relaxation of Isolated Many-Body Systems Which Do Not Thermalize

## TL;DR

This paper develops a general analytical theory describing how isolated many-body quantum systems that do not thermalize relax over time, explaining experimental and numerical observations across various models.

## Contribution

It introduces a universal analytical framework for the typical relaxation behavior of non-thermalizing many-body quantum systems, applicable to diverse experimental setups.

## Key findings

- Theory matches experimental results in trapped-ion quantum simulators.
- Theory explains relaxation in ultracold atomic gases.
- Consistent with numerical simulations of integrable models.

## Abstract

We consider isolated many-body quantum systems which do not thermalize, i.e., expectation values approach an (approximately) steady longtime limit which disagrees with the microcanonical prediction of equilibrium statistical mechanics. A general analytical theory is worked out for the typical temporal relaxation behavior in such cases. The main prerequisites are initial conditions which appreciably populate many energy levels and do not give rise to significant spatial inhomogeneities on macroscopic scales. The theory explains very well the experimental and numerical findings in a trapped-ion quantum simulator exhibiting many-body localization, in ultracold atomic gases, and in integrable hard-core boson and XXZ models.