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arXiv · 1107.0405

The BCS gap equation for spin-polarized fermions

Abraham Freiji·Christian Hainzl·Robert Seiringer
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Abstract

We study the BCS gap equation for a Fermi gas with unequal population of spin-up and spin-down states. For $\cosh(δ_μ/T) \leq 2$, with $T$ the temperature and $δ_μ$ the chemical potential difference, the question of existence of non-trivial solutions can be reduced to spectral properties of a linear operator, similar to the unpolarized case studied previously in \cite{FHNS,HHSS,HS}. For $\cosh(δ_μ/T) > 2$ the phase diagram is more complicated, however. We derive upper and lower bounds for the critical temperature, and study their behavior in the small coupling limit.

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Abraham Freiji, Christian Hainzl, Robert Seiringer. 2011-07-02. The BCS gap equation for spin-polarized fermions. https://doi.org/10.1063/1.3670747

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