# Thermalization in open many-body systems based on eigenstate thermalization hypothesis

## TL;DR

This paper explores how the eigenstate thermalization hypothesis (ETH) can predict the steady states of open quantum systems under weak dissipation, highlighting differences between bulk and boundary dissipation through theoretical and numerical analysis.

## Contribution

It establishes a criterion linking ETH, dissipation strength, and the validity of perturbation theory in describing steady states of open quantum systems.

## Key findings

- Gibbs state at an effective temperature describes steady states under ETH.
- Perturbation theory validity depends on system size and dissipation type.
- Numerical results confirm theoretical predictions about steady state behavior.

## Abstract

We investigate steady states of macroscopic quantum systems under dissipation not obeying the detailed balance condition. We argue that the Gibbs state at an effective temperature gives a good description of the steady state provided that the system Hamiltonian obeys the eigenstate thermalization hypothesis (ETH) and the perturbation theory in the weak system-environment coupling is valid in the thermodynamic limit. We derive a criterion to guarantee the validity of the perturbation theory, which is satisfied in the thermodynamic limit for sufficiently weak dissipation when the Liouvillian is gapped for bulk-dissipated systems, while the perturbation theory breaks down in boundary-dissipated chaotic systems due to the presence of diffusive transports. We numerically confirm these theoretical predictions. This work suggests a connection between steady states of macroscopic open quantum systems and the ETH.