Condensation of fermion pairs in a domain
Condensation of fermion pairs in a domain
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DOI：
10.1007/s00526-017-1140-x
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发表时间：
2017-04-01
影响因子：
2.1
通讯作者：
Simon, Barry
中科院分区：
文献类型：
--
作者：
Frank, Rupert L.;Lemm, Marius;Simon, Barry
我们考虑一种在零温度和低密度下的费米子气体，通过一个允许束缚态的微观两体势相互作用。粒子被限制在一个域的Dirichlet边界条件。本文从微观BCS理论出发，导出了描述费米子对凝聚的宏观Gross-Pitaevskii（GP）理论。GP理论也有Dirichlet边界条件。沿着的方式，我们证明了GP能量，定义与Dirichlet边界条件上的有界Lipschitz域，是连续的内部和外部的近似下，该区域。
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.