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Published April 2017 | Submitted
Journal Article Open

Condensation of fermion pairs in a domain

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.

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.

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August 19, 2023
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