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Quantum master equation from the eigenstate thermalization hypothesis
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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.
Forward citations
Cited by 4 Pith papers
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The ETH off-diagonal variance is decomposed exactly into a diagonal overlap baseline plus a multi-resolvent correlation series, whose third level generically generates odd-frequency skewness.
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Thermal and symmetry Mpemba effects are unified via resource theories, with symmetry restoration controlled by the initial overlap with the slowest symmetry-breaking mode.
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Non-Markovianity of subsystem dynamics in isolated quantum many-body systems
Quenching a mixed-field Ising chain from paramagnetic to ferromagnetic parameters makes small subsystems display strong non-Markovian, memory-retaining dynamics, while the reverse quench is nearly Markovian.
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Typical Positivity of Nonequilibrium Entropy Production for Pure States
For almost all pure states sampled from the Scrooge measure, entropy production is exponentially close to the ensemble value, so typical pure states obey the second law.
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