Results for pseudogaps are obtained from a band model, where the stability of the gap depends on the amplitudes of vibrational displacements, or magnetic moments, and their coupling to electrons. A one-particle gap is favored by normal thermal excitations of phonons or spin waves. Another gap can be generated by spontaneous waves at lower temperature, if the electronic energy gain overcomes the elastic/magnetic energy needed for increased amplitudes of the oscillations. This state is characterized by charge or spin density waves. The pseudogap has many features in common with the superconducting gap, and the model lends support to the interpretation that the pseudogap is a precursor of, and competes with, superconducting pairing.
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