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I present an exactly solvable model of a pseudogap with two zero-energyfermion modes coupled to each other by a classical source of frequency omega_0and strength |Delta|. A suitably defined fermion propagator has an infinitenumber of poles at frequencies that are multiple integers of omega_0. In theadiabatic limit, omega_0 << |\Delta|, the situation is qualitatively differentfrom the static case omega_0=0: the residue of the pole at omega=0 (a remnantof the bare fermion) vanishes linearly with omega_0, a result that could not beanticipated by perturbation theory; the multiple poles of the propagatorcoalesce into a continuum instead of forming two single poles at +-|Delta|,which should be interpreted as inhomogeneous broadening of the Bogoliubovquasiparticles.Comment: REVTeX, 8 pages, 2 PostScript figure

Pseudogaps: A third peak in the fermion spectral function