Relation between Feynman cycles and off-diagonal long-range order.
The usual order parameter for 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.
Ueltschi
Daniel
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Department of Mathematics, University of Arizona, Tucson, Arizona 85721, USA.