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

Tatsuhiko Shirai1, Takashi Mori2

  • 1Green Computing Systems Research Organization, Waseda University, Tokyo 162-0042, Japan.

Physical Review. E
|May 20, 2020
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We found that Gibbs states describe steady states in open quantum systems if the system Hamiltonian obeys the eigenstate thermalization hypothesis (ETH). This holds for weak dissipation, but breaks down for boundary-dissipated chaotic systems.

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Area of Science:

  • Quantum physics
  • Statistical mechanics
  • Condensed matter theory

Background:

  • Investigating steady states of macroscopic quantum systems under non-detailed-balance dissipation is crucial.
  • Understanding when these systems approach equilibrium is a key challenge.

Purpose of the Study:

  • To determine if Gibbs states with an effective temperature can describe non-equilibrium steady states.
  • To identify conditions for the validity of perturbation theory in open quantum systems.

Main Methods:

  • Theoretical analysis of macroscopic quantum systems under dissipation.
  • Derivation of a criterion for the validity of perturbation theory.
  • Numerical confirmation of theoretical predictions.

Main Results:

  • The Gibbs state with an effective temperature accurately describes steady states when the eigenstate thermalization hypothesis (ETH) holds and perturbation theory is valid.
  • Perturbation theory is valid in the thermodynamic limit for weak dissipation if the Liouvillian is gapped (bulk dissipation).
  • Perturbation theory breaks down in boundary-dissipated chaotic systems due to diffusive transport.

Conclusions:

  • A connection exists between steady states of macroscopic open quantum systems and the ETH.
  • The findings provide criteria for the applicability of equilibrium-like descriptions to non-equilibrium quantum systems.