一般对相互作用的BCS泛函
The BCS Functional for General Pair Interactions
摘要：
Bardeen-Cooper-Schrieffer（BCS）泛函作为描述费米气体与局部成对相互作用的一种方法，最近重新受到人们的关注。我们在这里提出了一个严格的分析BCS功能的一般对相互作用势。对于零温度和正温度，我们证明了非线性BCS带隙方程的非平凡解的存在性等价于某个线性算子的负本征值的存在性。由此我们得出结论，存在一个临界温度，低于该温度BCS对波函数不会完全消失。对于吸引势，我们证明了它的临界温度是非零的，并且在势的强度上是指数小的。
英文摘要：
The Bardeen-Cooper-Schrieffer (BCS) functional has recently received renewed attention as a description of fermionic gases interacting with local pairwise interactions. We present here a rigorous analysis of the BCS functional for general pair interaction potentials. For both zero and positive temperature, we show that the existence of a non-trivial solution of the nonlinear BCS gap equation is equivalent to the existence of a negative eigenvalue of a certain linear operator. From this we conclude the existence of a critical temperature below which the BCS pairing wave function does not vanish identically. For attractive potentials, we prove that the critical temperature is non-zero and exponentially small in the strength of the potential.
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