Formation of infinite loops for an interacting bosonic loop soup
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866916124143124480 |
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| author | Dickson, Matthew Vogel, Quirin |
| author_facet | Dickson, Matthew Vogel, Quirin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_01409 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Formation of infinite loops for an interacting bosonic loop soup Dickson, Matthew Vogel, Quirin Probability 60K35 (Primary), 60G50 (Secondary) 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. |
| title | Formation of infinite loops for an interacting bosonic loop soup |
| topic | Probability 60K35 (Primary), 60G50 (Secondary) |
| url | https://arxiv.org/abs/2109.01409 |