The relation between Feynman cycles and off-diagonal long-range order
Daniel Ueltschi
TL;DR
This paper explores the connection between Feynman cycles and off-diagonal long-range order in Bose-Einstein condensation, revealing that infinite cycles do not always indicate the presence of a condensate.
Contribution
It provides a formula linking Feynman cycles with off-diagonal long-range order and discusses its validity through rigorous and heuristic analysis.
Findings
Infinite cycles do not always correspond to Bose condensate.
A new formula relates Feynman cycles to off-diagonal correlations.
The validity of the relation is supported by rigorous and heuristic arguments.
Abstract
The usual order parameter for the Bose-Einstein condensation involves the off-diagonal correlation function of Penrose and Onsager, but an alternative is Feynman's notion of infinite cycles. We present a formula that relates both order parameters. We discuss its validity with the help of rigorous results and heuristic arguments. The conclusion is that infinite cycles do not always represent the Bose condensate.
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