Localization and interaction effects in anisotropic disordered electronic systems

Scale-dependent effects on the conductivity of anisotropic disordered metallic systems are discussed to lowest order in the inverse diffusion tensor $D_{\mu \nu }^{\mathrm{-}1}$ and in the interaction. An eigenfunction expansion for anisotropic scattering and many-body perturbation theory are used to show that, in two dimensions, the fractional-scale-dependent conductivity is independent of direction. One consequence is that the scaling function and critical behavior near the localization transition are unaffected by anisotropy. Comparison with experimental results, and mapping onto a field theory, are briefly discussed.