The relation between Feynman cycles and off-diagonal long-range order

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.

5 pages

References in corpus (1)

• Supersolids versus phase separation in two-dimensional lattice bosons

Cited by in corpus (4)

• Spatial random permutations and infinite cycles
• Feynman cycles in the Bose gas
• Long Cycles in the Infinite-Range-Hopping Bose-Hubbard Model with Hard Cores
• Large deviations for empirical path measures in cycles of integer partitions