Interacting loop ensembles and Bose gases
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866917445737906176 |
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| author | Fröhlich, Jürg Knowles, Antti Schlein, Benjamin Sohinger, Vedran |
| author_facet | Fröhlich, Jürg Knowles, Antti Schlein, Benjamin Sohinger, Vedran |
| contents | We study interacting Bose gases in thermal equilibrium on a lattice. We establish convergence of the grand canonical Gibbs states of such gases to their mean-field (classical field) and large-mass (classical particle) limits. The former is a classical field theory for a complex scalar field with quartic self-interaction. The latter is a classical theory of point particles with two-body interactions. Our analysis is based on representations in terms of ensembles of interacting random loops, the Ginibre loop ensemble for Bose gases and the Symanzik loop ensemble for classical scalar field theories. For small enough interactions, our results also hold in infinite volume. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2012_05110 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Interacting loop ensembles and Bose gases Fröhlich, Jürg Knowles, Antti Schlein, Benjamin Sohinger, Vedran Mathematical Physics Probability 60G60, 82B10, 81V70 We study interacting Bose gases in thermal equilibrium on a lattice. We establish convergence of the grand canonical Gibbs states of such gases to their mean-field (classical field) and large-mass (classical particle) limits. The former is a classical field theory for a complex scalar field with quartic self-interaction. The latter is a classical theory of point particles with two-body interactions. Our analysis is based on representations in terms of ensembles of interacting random loops, the Ginibre loop ensemble for Bose gases and the Symanzik loop ensemble for classical scalar field theories. For small enough interactions, our results also hold in infinite volume. |
| title | Interacting loop ensembles and Bose gases |
| topic | Mathematical Physics Probability 60G60, 82B10, 81V70 |
| url | https://arxiv.org/abs/2012.05110 |