A mathematical proof that the transition to a superconducting state is a second-order phase transition

Details A mathematical proof that the transition to a superconducting state is a second-order phase transition A mathematical proof that the transition to a superconducting state is a second-order phase transition

2008-08-26

arxiv.org/abs/0808.3438v1

Far East Journal of Mathematical Sciences, vol. 34 (2009), 37-57

Physics

Mathematical Physics

16 pages

Scientific paper

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 $C^2$ on the closed interval $[ 0, T_c ]$ and point out some more properties of the gap function. Here, $T_c$ 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.

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