Comparison of weakly inhomogeneous BCS- and Hubbard models

We compare the weakly inhomogeneous BCS-model of a previous investigation with a weak perturbation of a symmetrized Hubbard model in the pair formalism on the homogeneous lattice. In terms of our operator algebraic discussion we prove the existence of unique limiting Gibbs states at fixed particle density (and temperature) for both models (which guarantees the physical equivalence of the large finite models with their thermodynamic limit). A close similarity of the condensate structure between the two models is made explicit, especially the appearance of two critical densities. This likeness manifests itself also in the derived self-consistency equations for the momentum resp. position dependent, complex gap parameters. The results on a stable gap and macroscopic phase are thus transferable from the BCS- to this Hubbard model. Only the localization of the condensate of the Hubbard model at zero momentum bears some resemblance to the Bose-Einstein condensation.