  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.
