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Quantum Chaos, Random Matrices, and Irreversibility in Interacting Many-Body Quantum Systems
1Max-Planck-Institut für Kernphysik, D-69029 Heidelberg, Germany.
Entropy (Basel, Switzerland)
|July 27, 2022
Summary
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
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.
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