# Dynamical typicality of embedded quantum systems

## TL;DR

This paper demonstrates that the dynamics of a quantum system coupled to a large environment exhibit typicality, with the reduced density matrix self-averaging, which supports the use of averaging over random interactions and explains irreversibility.

## Contribution

The paper provides an analytical and numerical proof of the typicality of quantum system dynamics coupled to an environment, establishing a new ergodic principle for embedded quantum systems.

## Key findings

- Reduced density matrix exhibits self-averaging property.
- Supports averaging procedures over random interactions.
- Explains the robustness of thermalisation processes.

## Abstract

We consider the dynamics of an arbitrary quantum system coupled to a large arbitrary and fully quantum mechanical environment through a random interaction. We establish analytically and check numerically the typicality of this dynamics, in other words the fact that the reduced density matrix of the system has a self-averaging property. This phenomenon, which lies in a generalized central limit theorem, justifies rigorously averaging procedures over certain classes of random interactions and can explain the absence of sensitivity to microscopic details of irreversible processes such as thermalisation. It provides more generally a new ergodic principle for embedded quantum systems.