Pseudogaps in one-dimensional models with quasi-long-range order

We use analytic and numerical methods to determine the density of states of a one-dimensional electron gas coupled to a spatially random quasistatic b ackscattering potential of long correlation length. Our results provide ins ight into the ''pseudogap'' phenomenon occurring in underdoped high-T-c sup erconductors, quasi-one-dimensional organic conductors, and liquid metals. They demonstrate the important role played by amplitude fluctuations of the backscattering potential and by fluctuations in gradients of the potential , and confirm the importance of the self-consistency which is a key feature of the "fluctuation exchange'' type approximations for the electron Green' s function. Our results allow an assessment of the merits of different appr oximations: a previous approximate treatment presented by Sadovskii and, we show, justified by a WKB approximation gives a reasonably good representat ion, except for a ''central peak'' anomaly, of our numerically computed den sities of states, whereas a previous approximation introduced by Lee, Rice, and Anderson is not as accurate.