# Many-body dynamical localization and thermalization

## TL;DR

This paper demonstrates quantum dynamical localization in a system of two weakly-coupled chaotic Bose-Hubbard units, revealing localization effects in thermalization processes beyond classical chaos descriptions.

## Contribution

The study introduces an intrinsic localization measure based on initial condition memory, applicable to high-dimensional quantum systems where classical correspondence breaks down.

## Key findings

- Quantum localization observed in thermalization of coupled chaotic subsystems
- Localization persists near the mobility edge, suppressing ergodization
- Weak localization effects are identified despite high system dimensionality

## Abstract

We show that a quantum dynamical localization effect can be observed in a generic thermalization process of two weakly-coupled chaotic subsystems. Specifically, our model consists of the minimal experimentally relevant subsystems that exhibit chaos, which are 3-site Bose-Hubbard units. Due to the high dimensionality of the composite 6-site system, the quantum localization effect is weak and can not be resolved merely by the breakdown of quantum-to-classical correspondence. Instead, we adopt an intrinsic definition of localization as the memory of initial conditions, that is not related to the underlying classical dynamics. We discuss the dynamics in the chaotic sea, and in the vicinity of the mobility edge, beyond which ergodization is suppressed.