Quantum master equation from the eigenstate thermalization hypothesis

TL;DR

This paper derives a quantum master equation based on the eigenstate thermalization hypothesis, showing how Markovian dynamics and local detailed balance emerge in systems coupled to chaotic pure-state baths, extending open quantum systems theory.

Contribution

It introduces a novel derivation of the quantum master equation using ETH, connecting thermalization concepts with open quantum system dynamics for pure-state baths.

Findings

Markovianity is governed by the spectral function of ETH.

Local detailed balance emerges in the Markovian regime.

Numerical verification shows agreement with chaotic baths, disagreement with integrable baths.

Abstract

We use the eigenstate thermalization hypothesis to derive a quantum master equation for a system weakly coupled to a chaotic finite-sized bath prepared in a pure state. We show that the emergence of Markovianity is controlled by the spectral function of the ETH and that local detailed balance emerges in the Markovian regime for a broad class of pure bath states. We numerically verify this result by comparing the master equation to dynamics computed using exact diagonalization of a chaotic Hamiltonian. We also compare the master equation to exact dynamics for an integrable bath and find that at finite size they strongly disagree. Our work puts forward eigenstate thermalization as a foundation for open quantum systems theory, thus extending it beyond ensemble bath preparations to chaotic many-body environments in generic pure states.