We review the density of states and related quantities of quasi
one-dimensional disordered Peierls systems in which fluctuation effects of a
backscattering potential play a crucial role. The low-energy behavior of
non-interacting fermions which are subject to a static random backscattering
potential will be described by the fluctuating gap model (FGM). Recently, the
FGM has also been used to explain the pseudogap phenomenon in high-Tc
superconductors. After an elementary introduction to the FGM in the context of
commensurate and incommensurate Peierls chains, we develop a non-perturbative
method which allows for a simultaneous calculation of the density of states
(DOS) and the inverse localization length. First, we recover all known results
in the limits of zero and infinite correlation lengths of the random potential.
Then, we attack the problem of finite correlation lengths. While a complex
order parameter, which describes incommensurate Peierls chains, leads to a
suppression of the DOS, i.e. a pseudogap, the DOS exhibits a singularity at the
Fermi energy if the order parameter is real and therefore refers to a
commensurate system. We confirm these results by calculating the DOS and the
inverse localization length for finite correlation lengths and Gaussian
statistics of the backscattering potential with unprecedented accuracy
numerically. Finally, we consider the case of classical phase fluctuations
which apply to low temperatures where amplitude fluctuations are frozen out. In
this physically important regime, which is also characterized by finite
correlation lengths, we present analytic results for the DOS, the inverse
localization length, the specific heat, and the Pauli susceptibility.Comment: 60 pages, 16 figure
