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Equilibration of quantum chaotic systems.

Quntao Zhuang1, Biao Wu2

  • 1International Center for Quantum Materials, Peking University, Beijing 100871, China.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
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Summary
This summary is machine-generated.

The quantum ergodic theorem applies to chaotic quantum systems, showing they reach equilibrium. Quantum systems exhibit exponential fluctuations, unlike classical systems with Gaussian fluctuations.

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Area of Science:

  • Quantum mechanics
  • Statistical mechanics
  • Chaos theory

Background:

  • The quantum ergodic theorem, established by von Neumann and Reimann, describes the behavior of quantum systems.
  • Its applicability to quantum chaotic systems remains unclear, lacking rigorous proof.
  • Classical systems exhibit Gaussian fluctuations around equilibrium.

Purpose of the Study:

  • To verify the quantum ergodic theorem for quantum chaotic systems.
  • To investigate the dynamical relaxation and equilibrium properties of these systems.
  • To compare quantum fluctuations with classical fluctuations.

Main Methods:

  • Numerical simulations of quantum chaotic systems.
  • Analysis of system dynamics from low-entropy to equilibrium states.
  • Comparison of quantum equilibrium states with the classical microcanonical ensemble.

Main Results:

  • Quantum chaotic systems dynamically relax to a high-entropy equilibrium state.
  • The quantum equilibrium state closely resembles the classical microcanonical ensemble.
  • Quantum fluctuations around equilibrium are exponential, contrasting with classical Gaussian fluctuations.

Conclusions:

  • The quantum ergodic theorem is illustrated and verified for quantum chaotic systems.
  • Dynamical relaxation in quantum chaotic systems leads to an equilibrium state.
  • Distinct exponential quantum fluctuations differentiate these systems from classical counterparts.