Optical Conductivity and Pseudo Momentum Conservation in Anisotropic Fermi Liquids

Umklapp scattering determines the conductivity of clean metals. In typical quasi one dimensional Fermi liquids with an open Fermi surface, certain pseudo momenta do not decay by 2 particle collisions even in situations where Umklapp scattering relaxes the momentum of the quasi particles efficiently. Due to this approximate conservation of pseudo momentum, a certain fraction of the electrical current decays very slowly and a well pronounced low frequency peak emerges in the optical conductivity. We develop simple criteria to determine under what conditions approximate pseudomomentum conservation is relevant and calculate within in Fermi liquid theory the weights of the corresponding low frequency peaks and the temperature dependence of the various relevant decay rates. Based on these considerations, we obtain a qualitative picture of the frequency and temperature dependence of the optical conductivity of an anisotropic Fermi liquid.