Formation of infinite loops for an interacting bosonic loop soup
arXiv:2109.01409 · doi:10.1214/24-EJP1085
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.
arXiv comment36 pages, 6 figures
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