Chaos and thermalization in open quantum systems

TL;DR

This paper extends the eigenstate thermalization hypothesis to open quantum systems with Lindblad dynamics, introducing the Liouvillian ETH concept and demonstrating thermalization through chaos in driven-dissipative quantum models.

Contribution

It proposes a Liouvillian ETH framework for open quantum systems and validates it with random Liouvillians and a quantum spin chain, linking chaos to thermalization in dissipative settings.

Findings

Liouvillian ETH exhibits statistical properties similar to closed systems.

Thermalization occurs via suppression of coherent oscillations.

Chaotic dissipative dynamics obscure system responses.

Abstract

The eigenstate thermalization hypothesis (ETH) provides a cornerstone for understanding thermalization in isolated quantum systems, linking quantum chaos with statistical mechanics. In this work, we extend the ETH framework to open quantum systems governed by Lindblad dynamics. We introduce the concept of Liouvillian stripe (spectral subset of the non-Hermitian Liouvillian superoperator) which enables the definition of effective pseudo-Hermitian Hamiltonians. This construction allows us to conjecture a Liouvillian version of ETH, whereby local superoperators exhibit statistical properties akin to ETH in closed systems. We substantiate our hypothesis using both random Liouvillians and a driven-dissipative quantum spin chain, showing that thermalization manifests through the suppression of coherent oscillations and the emergence of structureless local dynamics. These findings have practical implications for the control and measurement of many-body open quantum systems, highlighting how chaotic dissipative dynamics can obscure the system response to external probes.