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This study derives the Pauli master equation for quantum system equilibration using quantum chaos and random-matrix theory. Equilibration arises from averaging over random matrices, with time

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Area of Science:

  • Quantum Physics
  • Statistical Mechanics
  • Quantum Chaos

Background:

  • The Pauli master equation is fundamental for describing statistical equilibration in closed quantum systems.
  • Previous approaches to deriving the equation have been simplified and generalized.

Purpose of the Study:

  • To present a novel derivation of the Pauli master equation.
  • To utilize concepts from quantum chaos and random-matrix theory for this derivation.

Main Methods:

  • Modeling the quantum system as an ensemble of random matrices, assuming strong internal mixing within subsystems.
  • Applying averaging over the random-matrix ensemble to achieve equilibration.
  • Quantifying conditions for the validity of the master equation, including smooth average level densities.

Main Results:

  • A generalized derivation of the Pauli master equation is presented.
  • The direction of the arrow of time is linked to a small coupling with the external environment.
  • Conditions for the master equation's validity at large times are established and quantified.

Conclusions:

  • The study provides a robust derivation of the Pauli master equation grounded in quantum chaos and random-matrix theory.
  • The findings clarify the role of subsystem mixing and external coupling in quantum equilibration.
  • The work establishes criteria for the applicability of the master equation and offers corrections for deviations.