Infinite cycles of interacting bosons

Abstract

In the first-quantized description of bosonic systems permutation cycles formed by the particles play a fundamental role. In the ideal Bose gas Bose-Enstein condensation (BEC) is signaled by the appearance of infinite cycles. When the particles interact, the two phenomena may not be simultaneous, the existence of infinite cycles is necessary but not sufficient for BEC. We demonstrate that their appearance is always accompanied by a singularity in the thermodynamic quantities which in three and four dimensions can be as strong as a one-sided divergence of the isothermal compressibility. Arguments are presented that long-range interactions can give rise to unexpected results, such as the absence of infinite cycles in three dimensions for long-range repulsion or their presence in one and two dimensions if the pair potential has a long attractive tail.

13 pages, minor changes

References in corpus (9)

• Spatial random permutations and infinite cycles
• Rigorous Upper Bound on the Critical Temperature of Dilute Bose Gases
• Feynman cycles in the Bose gas
• The relation between Feynman cycles and off-diagonal long-range order
• Formation of infinite loops for an interacting bosonic loop soup
• Long Cycles in the Infinite-Range-Hopping Bose-Hubbard Model with Hard Cores
• Large deviations analysis for random combinatorial partitions with counter terms
• Non Perturbative Renormalization Group and Bose-Einstein Condensation
• Bose-Einstein condensation of interacting bosons: A two-step proof