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Related Experiment Videos

Canonical typicality.

Sheldon Goldstein1, Joel L Lebowitz, Roderich Tumulka

  • 1Department of Mathematics, Hill Center, Rutgers, The State University of New Jersey, 110 Frelinghuysen Road, Piscataway, New Jersey 08854-8019, USA. oldstein@math.rutgers.edu

Physical Review Letters
|February 21, 2006
PubMed
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Quantum systems weakly coupled to a heat bath exhibit canonical ensemble behavior. This holds even for single wave functions, confirming and expanding upon Schrödinger's 1952 observations.

Area of Science:

  • Statistical Mechanics
  • Quantum Mechanics
  • Quantum Information Theory

Background:

  • Weakly coupled systems and heat baths are typically described by the canonical ensemble.
  • This description is valid when the composite system (S + B) is in the microcanonical ensemble.
  • Previous work established this for classical distributions and quantum density matrices.

Purpose of the Study:

  • To investigate if a stronger statement holds for quantum systems regarding ensemble descriptions.
  • To determine if a single wave function for the composite system leads to a canonical reduced density matrix for the subsystem.
  • To provide a rigorous justification for Schrödinger's 1952 remarks on this topic.

Main Methods:

  • Analysis of quantum systems weakly coupled to a heat bath.

Related Experiment Videos

  • Consideration of the composite system (S + B) described by a single wave function within a specific energy shell.
  • Derivation and examination of the reduced density matrix of the subsystem (S).

    • Main Results:

    • The reduced density matrix of the subsystem is canonical for the vast majority of wave functions.
    • This occurs even when the composite system's state is a single wave function, not a mixture.
    • The results apply to wave functions within the energy interval defined by the microcanonical ensemble.

    Conclusions:

    • A stronger quantum mechanical basis exists for the canonical ensemble description of weakly coupled systems.
    • The findings rigorously support and extend Schrödinger's early insights from 1952.
    • This work clarifies fundamental aspects of quantum statistical mechanics and the emergence of thermal equilibrium.