  We consider pseudogap effects for electrons interacting with gapless modes.
We study both generic 1D semiconductors with acoustic phonons and
incommensurate charge density waves. We calculate the subgap absorption as it
can be observed by means of the photo electron or tunneling spectroscopy.
Within the formalism of functional integration and the adiabatic approximation,
the probabilities are described by nonlinear configurations of an instanton
type. Particularities of both cases are determined by the topological nature of
stationary excited states (acoustic polarons or amplitude solitons) and by
presence of gapless phonons which change the usual dynamics to the regime of
the quantum dissipation. Below the free particle edge the pseudogap starts with
the exponential (stretched exponential for gapful phonons) decrease of
transition rates. Deeply within the pseudogap they are dominated by a power
law, in contrast with nearly exponential law for gapful modes.
