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Area of Science:

  • Quantum statistical mechanics
  • Condensed matter theory
  • Many-body quantum dynamics

Background:

  • Understanding the emergence of dissipation in isolated quantum systems is a key challenge.
  • Two-point correlation functions (dynamical response functions, Green's functions) are crucial for characterizing system dynamics.

Purpose of the Study:

  • To provide rigorous analytical results on the temporal behavior of two-point correlation functions in closed many-body quantum systems.
  • To demonstrate the emergence of dissipation from unitary dynamics and analyze fluctuations.
  • To establish bounds on relaxation timescales and connect them to emergent fluctuation-dissipation theorems.

Main Methods:

  • Analytical derivation of temporal behavior for two-point correlation functions.
  • Factorization properties of correlation functions at late times.
  • Bounding fluctuations by the purity of the thermal ensemble.
  • Derivation of an upper bound for relaxation timescales.

Main Results:

  • Demonstrated factorization of correlation functions at late times in translation-invariant models, proving emergent dissipation.
  • Showed that fluctuations are bounded by thermal ensemble purity, which decays exponentially with system size.
  • Provided a system-size-independent upper bound on the timescale for autocorrelation functions to reach their late-time value.
  • Numerical examples confirmed the bound's accuracy in nonintegrable models.

Conclusions:

  • Dissipation can emerge from the unitary evolution of closed quantum systems.
  • The derived bounds and emergent fluctuation-dissipation theorem offer a new perspective on thermalization and relaxation in quantum many-body systems.
  • The results extend to various two-point functions, including Kubo functions relevant to linear response theory.