Coupling of fluctuation modes in the disordered strongly attractive Hubbard model

The coupling of two different types of soft modes related to interaction-generated superconducting and disorder-generated (pseudo)diffusive fluctuations in the large negative-U Hubbard model with random local energies is studied in the framework of a Grassmann field theoretic approach with modified semionic Matsubara frequencies. In leading loop order it is found that the sound-like order parameter phase fluctuation mode retains its massless nature with only its velocity being modified, as expected from the generalized Ward identity. The disorder-induced fluctuations which are originally completely local due to the locality of disorder correlations acquire true diffusive behaviour by interaction effects in the superconducting phase.