A self-consistence equation describing a superconductor whose normal state is a Luttinger liquid is computed in a rigorous way by renormalization group techniques. The gap and the critical temperatures are quite different with respect to the ones of normal superconductors (i.e. superconductors whose normal state is a Fermi liquid) and in particular, the critical temperature can be quite high for suitable values of the parameters. Such self-consistence equation can be obtained in a BCS mean field theory for a model of two Mattis models exchanging Cooper pairs. The connection of this model with recent theories of high T c superconductivity is briefly discussed.
We study dynamic ground-state properties in the crossover from weak-(BCS) to strong-coupling (BEC) superfluidity. Our approach is based on the attractive Hubbard model which is analyzed by the dynamical mean-field theory (DMFT) combined with the numerical renormalization group (NRG). We present an extension of the NRG method for effective impurity models to self-consistent calculations with superconducting symmetry breaking. In the one-particle spectra we show quantitatively how the Bogoliubov quasiparticles at weak coupling become suppressed at intermediate coupling. We also present results for the spin and charge gap. The extension of the NRG method to self-consistent superconducting solutions opens the possibility to study a range of other important applications.