论文标题
BCS-Bogoliubov超导性模型中特定热量和临界磁场的操作者理论研究
An operator-theoretical study of the specific heat and the critical magnetic field in the BCS-Bogoliubov model of superconductivity
论文作者
论文摘要
在上一篇文章中，引入截止值，本作者证明了以下陈述：向超导状态的过渡是BCS-Bogoliubov超导率模型中的二阶相变，该模型是根据固定点定理的，并解决了从算法的角度的二阶过渡的长期存在的问题。在本文中，我们从操作员理论的角度研究了模型中特定热量和临界磁场的温度依赖性。我们首先显示了有关温度的BCS-Bogoliubov间隙方程的某些特性，并给出特定热量中间隙的确切和明确表达，除以特定热量。然后，我们证明它不取决于超导体，并且是通用常数。此外，我们表明临界磁场相对于温度平滑，并指出临界磁场及其导数的行为。
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.
