自旋极化费米子的BCS带隙方程
The BCS gap equation for spin-polarized fermions
摘要：
研究了自旋上、下态布居数不等的费米气体的BCS带隙方程。对于$\cosh(δ_μ/T) \leq 2$，与$T$的温度和$δ_μ$的化学电势差，非平凡的解决方案的存在性的问题可以减少到一个线性算子的光谱特性，类似于非极化的情况下，以前在\cite{FHNS,HHSS,HS}研究。然而，对于$\cosh(δ_μ/T) > 2$，相图更为复杂。我们推导出了临界温度的上、下界，并研究了它们在小耦合极限下的行为。
英文摘要：
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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