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2013 The Solution to the BCS Gap Equation for Superconductivity and Its Temperature Dependence
Shuji Watanabe
Abstr. Appl. Anal. 2013(SI13): 1-5 (2013). DOI: 10.1155/2013/932085

Abstract

From the viewpoint of operator theory, we deal with the temperature dependence of the solution to the BCS gap equation for superconductivity. When the potential is a positive constant, the BCS gap equation reduces to the simple gap equation. We first show that there is a unique nonnegative solution to the simple gap equation, that it is continuous and strictly decreasing, and that it is of class C2 with respect to the temperature. We next deal with the case where the potential is not a constant but a function. When the potential is not a constant, we give another proof of the existence and uniqueness of the solution to the BCS gap equation, and show how the solution varies with the temperature. We finally show that the solution to the BCS gap equation is indeed continuous with respect to both the temperature and the energy under a certain condition when the potential is not a constant.

Citation

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Shuji Watanabe. "The Solution to the BCS Gap Equation for Superconductivity and Its Temperature Dependence." Abstr. Appl. Anal. 2013 (SI13) 1 - 5, 2013. https://doi.org/10.1155/2013/932085

Information

Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 07095509
MathSciNet: MR3096829
Digital Object Identifier: 10.1155/2013/932085

Rights: Copyright © 2013 Hindawi

Vol.2013 • No. SI13 • 2013
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