Smoothness and Monotone Decreasingness of the Solution to the BCS-Bogoliubov Gap Equation for Superconductivity Pages 17-25

Smoothness and Monotone Decreasingness of the Solution to the BCS-Bogoliubov Gap Equation for Superconductivity
Pages 17-25Creative Commons License

Shuji Watanabe and Ken Kuriyama
DOI: https://doi.org/10.6000/1927-5129.2017.13.04
Published: 01 March 2017

Abstract: We show the temperature dependence such as smoothness and monotone decreasingness with respect to the temperature of the solution to the BCS-Bogoliubov gap equation for superconductivity. Here the temperature belongs to the closed interval [0,t] with t >0 nearly equal to half of the transition temperature. We show that the solution is continuous with respect to both the temperature and the energy, and that the solution is Lipschitz continuous and monotone decreasing with respect to the temperature. Moreover, we show that the solution is partially differentiable with respect to the temperature twice and the second-order partial derivative is continuous with respect to both the temperature and the energy, or that the solution is approximated by such a smooth function.

Keywords: Smoothness, monotone decreasingness, temperature, solution to the BCS-Bogoliubov gap equation, superconductivity.