Pairing gap equation weak coupling

Maliphus

In the limit of weak coupling, [itex]G\overline{ρ}<<1[/itex], the BCS pairing gap equation gives that [itex]Δ \propto exp(-1/G\overline{ρ})[/itex]. [itex]\overline{ρ}[/itex] is the level density.This cannot be developed as a power series in the interaction strength G. Does this imply that there is a phase transition between a superfluid and a normal fluid state? If so, how exactly?

DrDu

Yes, there is a phase transition. The order parameter is the cooper pair density and the phase transition breaks electromagnetic U(1) symmetry (in the case of superconductors). The mechanism has been transfered to other systems, so the symmetry broken, and the particles forming the condensate will depend on the system.