Notion of a pseudogap refers to systems where gaps in electronic spectra are only partly established showing subgap tails. Pseudogaps attract much attention in physics of strongly correlated systems: from High-Tc superconductors to Charge Density Wave CDW materials. We consider quasi one-dimensional systems where the gap is originated by spontaneous lattice distortions (Peierls effect) like in CDWs or in polyacethylene, as well as generically gapfull systems like conjugated polymers, semiconducting nanotubes and quantum wires. Their common property is a deep selftraping of electrons and their pairs into solitons, polarons, bipolarons. Further effects of ground states degeneracy come from a topological nature of excitations (amplitude solitons in CDWs, acoustic polarons otherwise) and from gapless phasons or phonons which change the usual dynamics to the regime of the quantum dissipation. In the frame of functional integration and within the adiabatic approximation, the probabilities are given by nonlinear configurations of an instanton type. We consider subgap transitions for photo electron spectroscopy, optics and tunneling. Thus for the internal coherent tunneling we calculate the interchain current both in single electron (polarons, amplitude solitons) and bi-particle (bipolarons, phase solitons) channels. We shall also review experiments demonstrating subgap spectra.

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