Pseudogap in the one-electron spectral functions of the attractive   Hubbard model
  We calculate the one-electron Green's function of the 2D attractive Hubbard model by coupling the electrons to pair fluctuations. The latter are approximated by homogeneous amplitude fluctuations and phase correlations corresponding to the XY-model. The electronic density of states shows a pseudogap at temperatures well above the transition temperature $T_{C}$. For a quasi-3D system, a superconducting gap emerges out of the pseudogap below $T_{C}$. 
Massimiliano Capezzali and Hans Beck