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Related Experiment Videos

Relation between Feynman cycles and off-diagonal long-range order.

Daniel Ueltschi1

  • 1Department of Mathematics, University of Arizona, Tucson, Arizona 85721, USA.

Physical Review Letters
|December 13, 2006
PubMed
Summary
This summary is machine-generated.

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Feynman

Area of Science:

  • Quantum mechanics
  • Statistical mechanics

Background:

  • Bose-Einstein condensation is typically characterized by the Penrose-Onsager off-diagonal correlation function.
  • An alternative proposed measure for Bose-Einstein condensation is Feynman's concept of infinite cycles.

Purpose of the Study:

  • To present a unifying formula relating the Penrose-Onsager and Feynman order parameters.
  • To rigorously assess the validity and applicability of Feynman's infinite cycles as a measure of Bose-Einstein condensation.

Main Methods:

  • Derivation of a novel formula connecting two distinct Bose-Einstein condensation order parameters.
  • Application of rigorous mathematical proofs and heuristic arguments to validate the formula.

Main Results:

Related Experiment Videos

  • A formula is established that explicitly links the Penrose-Onsager correlation function and Feynman's infinite cycles.
  • The study demonstrates that Feynman's infinite cycles are not universally equivalent to the Bose condensate.

    • Conclusions:

    • The presented formula provides a direct relationship between established and alternative measures of Bose-Einstein condensation.
    • Infinite cycles are shown to be an insufficient indicator for Bose-Einstein condensation in all cases, highlighting the primacy of the Penrose-Onsager parameter.