2010/08/31 by Shuji Watanabe
Physics and Astronomy · Mathematics · #math-ph #cond-mat.supr-con #math.FA #math.MP #msc:45G05 #msc:47H10 #msc:47N50 #msc:82D55
paper · pdf · doi:10.1016/j.jmaa.2013.03.070
published as Journal of Mathematical Analysis and Applications, Vol.405 (2013), 742-745 · Journal of Mathematical Analysis and Applications, in press. The new title is "Addendum to `The solution to the BCS gap equation and the second-order phase transition in superconductivity' ". arXiv admin note: substantial text overlap with arXiv:1006.0765
arxiv created 2013/04/02 · arxiv updated 2013/09/02
One of long-standing problems in mathematical studies of superconductivity is to show that the solution to the BCS gap equation is continuous in the temperature. In this paper we address this problem. We regard the BCS gap equation as a nonlinear integral equation on a Banach space consisting of continuous functions of both T and x. Here, T (≥ 0) stands for the temperature and x the kinetic energy of an electron minus the chemical potential. We show that the unique solution to the BCS gap equation obtained in our recent paper is continuous with respect to both T and x when T is small enough. The proof is carried out based on the Banach fixed-point theorem.