Theory of pseudogaps in charge density waves in application to photo electron or tunneling spectroscopy

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For a one-dimensional electron-phonon system we consider the photon absorption involving electronic excitations within the pseudogap energy range. In the framework of the adiabatic approximation for the electron - phonon interactions these processes are described by nonlinear configurations of an instanton type. We calculate the subgap absorption as it can be observed by means of photo electron or tunneling spectroscopies. In details we consider systems with gapless modes: 1D semiconductors with acoustic phonons and incommensurate charge density waves. We find that below the free particle edge the pseudogap starts with the exponential decrease of transition rates changing to a power law deeply within the pseudogap, near the absolute edge.