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Typicality for generalized microcanonical ensembles [corrected].

Peter Reimann1

  • 1Universität Bielefeld, Fakultät für Physik, 33615 Bielefeld, Germany.

Physical Review Letters
|November 13, 2007
PubMed
Summary
This summary is machine-generated.

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Quantum systems in unknown states exhibit predictable behavior, closely matching ensemble averages. This applies to both equilibrium and nonequilibrium conditions, even with complex microscopic details.

Area of Science:

  • Quantum mechanics
  • Statistical mechanics
  • Thermodynamics

Background:

  • Macroscopic quantum systems are often described by ensemble averages.
  • Understanding the behavior of isolated quantum systems in unknown pure states is crucial.
  • The role of microscopic details in macroscopic properties needs clarification.

Purpose of the Study:

  • To demonstrate that expectation values in macroscopic quantum systems rarely deviate from ensemble averages.
  • To investigate this phenomenon under both equilibrium and nonequilibrium conditions.
  • To explore the recovery of the canonical ensemble for subsystems.

Main Methods:

  • Analysis of macroscopic, isolated quantum systems in unknown pure states.
  • Consideration of uncontrollable microscopic details.

Related Experiment Videos

  • Investigation of subsystems coupled to a large heat bath.

    • Main Results:

    • Expectation values of observables show minimal deviation from ensemble averages with high probability.
    • This holds true for generic equilibrium and nonequilibrium conditions.
    • The canonical ensemble is recovered for subsystems under more general assumptions.

    Conclusions:

    • Macroscopic quantum systems behave predictably, aligning with ensemble averages.
    • The findings offer a more robust foundation for statistical mechanics in quantum systems.
    • The study provides a more realistic framework for describing subsystems in thermal contact.