Smoothness of the Gap Function in the BCS-Bogoliubov Theory of Superconductivity
Abstract
We deal with the gap equation in the BCS-Bogoliubov theory of superconductivity, where the gap function is a function of the temperature T only. We show that the squared gap function is of class C2 on the closed interval [\,0,\,Tc\,]. Here, Tc stands for the transition temperature. Furthermore, we show that the gap function is monotonically decreasing on [0,\,Tc] and obtain the behavior of the gap function at T=Tc. We mathematically point out some more properties of the gap function.
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