An operator-theoretical study on the BCS-Bogoliubov model of superconductivity near absolute zero temperature

TL;DR

This paper analyzes the behavior of superconducting properties near absolute zero temperature using operator theory, extending previous work on the BCS-Bogoliubov model by considering arbitrary potentials.

Contribution

It provides a detailed operator-theoretic analysis of the low-temperature behavior of superconductivity, including entropy, specific heat, and critical magnetic field, for general potentials.

Findings

Entropy and specific heat behavior near absolute zero

Dependence of critical magnetic field on temperature

Extension to arbitrary positive continuous potentials

Abstract

In the preceding papers the present author gave another proof of the existence and uniqueness of the solution to the BCS-Bogoliubov gap equation for superconductivity from the viewpoint of operator theory, and showed that the solution is partially differentiable with respect to the temperature twice. Thanks to these results, we can indeed partially differentiate the solution and the thermodynamic potential with respect to the temperature twice so as to obtain the entropy and the specific heat at constant volume of a superconductor. In this paper we show the behavior near absolute zero temperature of the thus-obtained entropy, the specific heat, the solution and the critical magnetic field from the viewpoint of operator theory since we did not study it in the preceding papers. Here, the potential in the BCS-Bogoliubov gap equation is an arbitrary, positive continuous function and need not be a constant.