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Quantum master equation from the eigenstate thermalization hypothesis

Peter O'Donovan1,*, Philipp Strasberg2,3, Kavan Modi4,5, John Goold1,6, and Mark T. Mitchison1,7,†

  • *Contact author: peodonov@tcd.ie
  • †Contact author: mark.mitchison@kcl.ac.uk
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Phys. Rev. B 112, 014312 – Published 22 July, 2025

DOI: https://doi.org/10.1103/kh96-ct3y

Abstract

We use the eigenstate thermalization hypothesis to derive a quantum master equation for a system that is 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.

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Phys. Rev. B 112, 014312– Published 22 July, 2025
  • Received 25 November 2024
  • Revised 21 May 2025
  • Accepted 13 June 2025
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