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.
Acknowledgments
The authors would like to thank the anonymous referees for their many suggestions. Quirin Vogel would like to thank Julius Damarackas for his help with improving the presentation of the article. He would further like to thank Roberto Fernandez, Vedran Sohinger and Daniel Ueltschi for the discussions on this topic.
Citation
Matthew Dickson. Quirin Vogel. "Formation of infinite loops for an interacting bosonic loop soup." Electron. J. Probab. 29 1 - 39, 2024. https://doi.org/10.1214/24-EJP1085
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