A pair potential supporting a mixed mean-field / BCS- phase

Abstract

We construct a Hamiltonian which in a scaling limit becomes equivalent to one that can be diagonalized by a Bogoliubov transformation. There may appear simultaneously a mean-field and a superconducting phase. They influence each other in a complicated way. For instance, an attractive mean field may stimulate the superconducting phase and a repulsive one may destroy it.