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The solution to the BCS gap equation and the second-order phase transition in superconductivity. (English) Zbl 1223.82074
The first part of the present paper is devoted to an alternative proof of the existence of a unique solution to the BCS gap equation. Next, it is defined a certain subspace W of a Banach space consisting of continuous functions and it is considered the solution approximated by an element of W. Next, it is shown that, under this approximation, the transition to a superconducting state is a second-order phase transition. In other words, it is established that the condition that the solution belongs to W is a sufficient condition for the second-order phase transition to superconductivity.
82D55Superconductors (statistical mechanics)
82B26Phase transitions (general)
45G10Nonsingular nonlinear integral equations
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