COMPARISON OF WEAKLY INHOMOGENEOUS BCS-MODEL AND HUBBARD-MODEL

We compare the weakly inhomogeneous BCS-model of a previous investigat ion with a weak perturbation of a symmetrized Hubbard model in the pai r formalism on the homogeneous lattice. In terms of our operator algeb raic discussion we prove the existence of unique limiting Gibbs states at fixed particle density (and temperature) for both models (which gu arantees physical equivalence of the large finite models with their th ermodynamic limit), A close similarity of the condensate structure bet ween the two models is made explicit, especially the appearance of two critical densities. This likeness manifests itself also in the derive d 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 moment um bears some resemblance to the Bose-Einstein condensation.