Formation of infinite loops for an interacting bosonic loop soup

Abstract

We compute the limiting measure for the Feynman loop representation of the Bose gas for a non mean-field energy. As predicted in previous works, for high densities the limiting measure gives positive weight to random interlacements, indicating the quantum Bose--Einstein condensation. We prove that in many cases there is a shift in the critical density compared to the free/mean-field case, and that in these cases the density of the random interlacements has a jump-discontinuity at the critical point.

36 pages, 6 figures

References in corpus (5)

• Spatial random permutations and infinite cycles
• A variational formula for the free energy of an interacting many-particle system
• Feynman cycles in the Bose gas
• Emergence of interlacements from the finite volume Bose soup
• Large deviations analysis for random combinatorial partitions with counter terms

Cited by in corpus (2)

• Coexistence, enhancements and short loops in random walk loop soups
• Infinite cycles of interacting bosons