Spectral density and density of states in a superconductor in an exactly solvable model of a pseudogap state

A simple, exactly solvable model of a pseudogap state induced by fluctuations of dielectric short-range order is used to study the peculiarities of the electronic spectral density and density of states of a superconductor in the model of the Fermi surface with hot patches. The problem is considered for arbitrary values of the short-range order correlation length ξ_corr. It is shown that the absence of self-averaging of the superconducting order parameter over the random field of dielectric fluctuations causes the spectral density and density of states to change significantly. The superconducting character of these quantities persists in a wide temperature range above the temperature T _c of the superconducting transition, which is uniform over the whole sample.