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Condensation of fermion pairs in a domain

Frank, Rupert L. and Lemm, Marius and Simon, Barry (2017) Condensation of fermion pairs in a domain. Calculus of Variations and Partial Differential Equations, 56 . Art. No. 54. ISSN 0944-2669. https://resolver.caltech.edu/CaltechAUTHORS:20170428-160716872

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Abstract

We consider a gas of fermions at zero temperature and low density, interacting via a microscopic two-body potential which admits a bound state. The particles are confined to a domain with Dirichlet boundary conditions. Starting from the microscopic BCS theory, we derive an effective macroscopic Gross–Pitaevskii (GP) theory describing the condensate of fermion pairs. The GP theory also has Dirichlet boundary conditions. Along the way, we prove that the GP energy, defined with Dirichlet boundary conditions on a bounded Lipschitz domain, is continuous under interior and exterior approximations of that domain.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1007/s00526-017-1140-xDOIArticle
http://link.springer.com/article/10.1007%2Fs00526-017-1140-xPublisherArticle
https://arxiv.org/abs/1608.01088arXivDiscussion Paper
ORCID:
AuthorORCID
Simon, Barry0000-0003-2561-8539
Additional Information:© 2017 Springer-Verlag Berlin Heidelberg. Received: 4 August 2016; Accepted: 20 February 2017; Published online: 3 April 2017. The authors would like to thank Christian Hainzl and Robert Seiringer for helpful discussions and the anonymous referee for useful remarks. R.L.F. was supported by the U.S. National Science Foundation through Grants PHY-1347399 and DMS-1363432. B.S. was supported by the U.S. National Science Foundation through Grant DMS-1265592 and by the Israeli Binational Science Foundation through Grant 2014337.
Funders:
Funding AgencyGrant Number
NSFPHY-1347399
NSFDMS-1363432
NSFDMS-1265592
Binational Science Foundation (USA-Israel)2014337
Classification Code:Mathematics Subject Classification: 82D50; 46N50; 81Q10
Record Number:CaltechAUTHORS:20170428-160716872
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170428-160716872
Official Citation:Frank, R.L., Lemm, M. & Simon, B. Calc. Var. (2017) 56: 54. doi:10.1007/s00526-017-1140-x
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77074
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:28 Apr 2017 23:40
Last Modified:03 Oct 2019 17:53

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