Fluctuation induced non-canonical BCS states: a mechanism for pseudogap

We pose the question of what effect the statistical fluctuation causes if it induces a non-unitary evolution. We apply this idea to the BCS model and study fluctuation around the mean-field average. We find that, dynamics of the thermalization influences the equilibrium besides the non-unitary evolution, and the resulting equilibrium state is no longer the canonical one. The pseudogap phenomenon can exist in this model.