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Far East Journal of Mathematical Sciences (FJMS)

on the closed interval

and point out some more properties of the gap function. Here,

stands for the transition temperature. On the basis of this study we then give, examining the thermodynamical potential, a mathematical proof that the transition to a superconducting state is a second-order phase transition. Furthermore, we obtain a new and more precise form of the gap in the specific heat at constant volume from a mathematical point of view.

Far East Journal of Mathematical Sciences (FJMS)
Volume 34, Issue 1, Pages 37 - 57 (July 2009)

A MATHEMATICAL PROOF THAT THE TRANSITION TO A SUPERCONDUCTING STATE IS A SECOND-ORDER PHASE TRANSITION
Shuji Watanabe (Japan)

Abstract:
We deal with the gap function and the thermodynamical potential in the BCS-Bogoliubov theory of superconductivity, where the gap function is a function of the temperature T only. We show that the squared gap function is of class

on the closed interval

and point out some more properties of the gap function. Here,

stands for the transition temperature. On the basis of this study we then give, examining the thermodynamical potential, a mathematical proof that the transition to a superconducting state is a second-order phase transition. Furthermore, we obtain a new and more precise form of the gap in the specific heat at constant volume from a mathematical point of view.

Keywords and phrases: second-order phase transition, superconductivity, gap function, thermodynamical potential.

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