Optical Conductivity in a Two - Dimensional Model of the Pseudogap State

We consider a two-dimensional model of the pseudogap state, based on the scenario of strong electron scattering by fluctuations of ``dielectric'' (AFM, CDW) short-range order. We construct a system of recurrence equations both for one-particle Green's function and vertex part, describing electron interaction with an external field, which take into account all Feynman graphs for electron scattering by short-range order fluctuations. The results of detailed calculations of optical conductivity are presented for different geometries (topologies) of the Fermi surface, demonstrating both the effects of pseudogap formation and localization effects. These results are in qualitative agreement with experimental data obtained for high-temperature superconducting cuprates.