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Interacting loop ensembles and Bose gases
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Fröhlich, Jürg, Knowles, Antti, Schlein, Benjamin and Sohinger, Vedran (2023) Interacting loop ensembles and Bose gases. Annales Henri Poincare, 24 . pp. 1439-1503. doi:10.1007/s00023-022-01238-1 ISSN 1424-0637.
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Official URL: https://doi.org/10.1007/s00023-022-01238-1
Abstract
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. The results of this paper were previously sketched in Fröhlich et al. (J Stat Phys 180(1–6):810–831, 2020).
Item Type: | Journal Article | ||||||||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||
Journal or Publication Title: | Annales Henri Poincare | ||||||||||||
Publisher: | Springer Basel AG | ||||||||||||
ISSN: | 1424-0637 | ||||||||||||
Official Date: | May 2023 | ||||||||||||
Dates: |
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Volume: | 24 | ||||||||||||
Number of Pages: | 65 | ||||||||||||
Page Range: | pp. 1439-1503 | ||||||||||||
DOI: | 10.1007/s00023-022-01238-1 | ||||||||||||
Status: | Peer Reviewed | ||||||||||||
Publication Status: | Published | ||||||||||||
Reuse Statement (publisher, data, author rights): | This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s00023-022-01238-1 | ||||||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||||||
Copyright Holders: | Springer Nature Switzerland AG | ||||||||||||
Date of first compliant deposit: | 30 May 2023 | ||||||||||||
Date of first compliant Open Access: | 19 October 2023 | ||||||||||||
RIOXX Funder/Project Grant: |
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