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Universal fluctuations around typicality for quantum ergodic systems.

Michel Bauer1,2, Denis Bernard3, Tony Jin3

  • 1Institut de Physique Théorique de Saclay, CEA-Saclay and CNRS, 91191 Gif-sur-Yvette, France.

Physical Review. E
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Summary
This summary is machine-generated.

Quantum systems in large volumes with noisy dynamics tend towards mixed states. Fluctuations around this are described by random matrix theory, specifically the Gaussian unitary ensemble (GUE).

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Area of Science:

  • Quantum statistical mechanics
  • Quantum chaos
  • Random matrix theory

Background:

  • Macroscopically large quantum systems in pure states with ergodic dynamics exhibit thermalization.
  • The reduced density matrix of subsystems approaches a mixed state, a concept known as typicality.

Purpose of the Study:

  • To analyze fluctuations around the totally mixed state for subsystems in large quantum systems.
  • To investigate fluctuations around the canonical Gibbs state under energy-conserving dynamics.

Main Methods:

  • Analysis of unitary dynamics in large quantum systems.
  • Application of random matrix theory, specifically the Gaussian unitary ensemble (GUE).
  • Investigation of energy-conserving unitary transformations on energy shells.

Main Results:

  • Fluctuations around the totally mixed state are captured by the GUE.
  • Fluctuations around the canonical Gibbs state are described by a deformed GUE, with covariance linked to the Gibbs state.

Conclusions:

  • The GUE and its deformations provide a framework for understanding thermalization and fluctuations in quantum systems.
  • This work connects random matrix theory to the eigenstate thermalization hypothesis.