Abstract
In the preceding paper, introducing a cutoff, the present author gave a proof of the statement that the transition to a superconducting state is a second-order phase transition in the BCS-Bogoliubov model of superconductivity on the basis of fixed-point theorems, and solved the long-standing problem of the second-order phase transition from the viewpoint of operator theory. In this paper we study the temperature dependence of the specific heat and the critical magnetic field in the model from the viewpoint of operator theory. We first show some properties of the solution to the BCS-Bogoliubov gap equation with respect to the temperature, and give the exact and explicit expression for the gap in the specific heat divided by the specific heat. We then show that it does not depend on superconductors and is a universal constant. Moreover, we show that the critical magnetic field is smooth with respect to the temperature, and point out the behavior of both the critical magnetic field and its derivative. Mathematics Subject Classification 2010. 45G10, 47H10, 47N50, 82D55.
Highlights
In this paper we introduce a cutoff and study the temperature dependence both of the specific heat at constant volume and of the critical magnetic field in the BCS-Bogoliubov model of superconductivity from the viewpoint of operator theory
On the basis of fixed-point theorems, we first show some properties of the solution with respect to the absolute temperature T both at sufficiently small T and at T in the neighborhood of the transition temperature specific heat
We show that the critical magnetic field applied to type-I superconductors is of class C1 both with respect to sufficiently small T and with respect to T in the neighborhood of the transition temperature Tc. We show (Tc), and point out the behavior of the critical magnetic field and its derivative
Summary
In the preceding paper, introducing a cutoff, the present author gave a proof of the statement that the transition to a superconducting state is a second-order phase transition in the BCS-Bogoliubov model of superconductivity on the basis of fixed-point theorems, and solved the long-standing problem of the second-order phase transition from the viewpoint of operator theory. On the basis of fixed-point theorems, the present author 1 [Theorems 2.3 and 2.4] introduced a cutoff and showed that the solution is partially differentiable with respect to the temperature twice, and gave an operator-theoretical proof of the statement that the transition from a normal conducting state to a superconducting state is a second-order phase transition. The present author 1 [Theorems 2.3 and 2.4] showed that the solution is partially differentiable with respect to T (in the neighborhood of the transition temperature Tc) twice, www.nature.com/scientificreports and gave a proof of the statement that the transition from a normal conducting state to a superconducting state is a second-order phase transition from the viewpoint of operator theory.
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