论文标题
BCS-Bogoliubov超导性模型中二阶过渡的另一个操作员理论证明
Another operator-theoretical proof for the second-order phase transition in the BCS-Bogoliubov model of superconductivity
论文作者
论文摘要
在前面的论文中，施加了某些复杂和强的条件，本作者表明，超导性中BCS-Bogoliubov差距方程的解决方案仅在绝对零温度和过渡温度的邻域中有两倍的差异性，以表明从操作机理论的角度来看，相位转变是第二阶。取而代之的是，我们在本文中施加了一定的简单和弱条件，并表明存在独特的非负解决方案，并且该解决方案的确在从一定的正温度到过渡温度的封闭间隔上差异两倍，并指出了解决方案的几个特性。然后，我们为BCS-Bogoliubov模型中的二阶相变提供了另一个操作器理论证明。由于热力学电势具有其形式的平方溶液，因此我们处理平方BCS-Bogoliubov间隙方程。在这里，BCS-Bogoliubov间隙方程中的电势是一个函数，不必是常数。
In the preceding papers, imposing certain complicated and strong conditions, the present author showed that the solution to the BCS-Bogoliubov gap equation in superconductivity is twice differentiable only on the neighborhoods of absolute zero temperature and the transition temperature so as to show that the phase transition is of the second order from the viewpoint of operator theory. Instead, we impose a certain simple and weak condition in this paper, and show that there is a unique nonnegative solution and that the solution is indeed twice differentiable on a closed interval from a certain positive temperature to the transition temperature as well as pointing out several properties of the solution. We then give another operator-theoretical proof for the second-order phase transition in the BCS-Bogoliubov model. Since the thermodynamic potential has the squared solution in its form, we deal with the squared BCS-Bogoliubov gap equation. Here, the potential in the BCS-Bogoliubov gap equation is a function and need not be a constant.
