BCS能隙方程的解与超导中的二级相变
The solution to the BCS gap equation and the second-order phase transition in superconductivity
摘要：
超导BCS能隙方程的解的存在唯一性已在前人的文献中得到了证明，但没有讨论解的温度依赖性。为了说明解随温度的变化，本文首先给出了解的存在唯一性的另一种证明，并指出唯一解属于某个集合。这里，该设置取决于温度$T$。定义了由$T$和$x$的连续函数组成的Banach空间的另一个子集。这里，$x$代表电子的动能减去化学势。让解决方案是近似的一个元素的子集的Banach空间以上。在这种近似下，我们证明了到超导态的转变是一个二级相变。
英文摘要：
The existence and the uniqueness of the solution to the BCS gap equation of superconductivity is established in previous papers, but the temperature dependence of the solution is not discussed. In this paper, in order to show how the solution varies with the temperature, we first give another proof of the existence and the uniqueness of the solution and point out that the unique solution belongs to a certain set. Here this set depends on the temperature $T$. We define another certain subset of a Banach space consisting of continuous functions of both $T$ and $x$. Here, $x$ stands for the kinetic energy of an electron minus the chemical potential. Let the solution be approximated by an element of the subset of the Banach space above. We second show, under this approximation, that the transition to a superconducting state is a second-order phase transition.
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