Is the solution to the BCS gap equation continuous in the temperature ?

Abstract

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, $T(\ge 0)$ 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.

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

References in corpus (4)

• Critical Temperature and Energy Gap for the BCS Equation
• The BCS Functional for General Pair Interactions
• The solution to the BCS gap equation and the second-order phase transition in superconductivity
• Superconductivity and the BCS-Bogoliubov Theory

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