We calculate the average conductivity $\sigma \left(\omega \right)$ of interacting electrons in one dimension in the presence of a long-range random potential (forward scattering disorder). Taking the curvature of the energy dispersion into account, we show that weak disorder leads to a transport scattering rate that vanishes as ${\omega }^2$ for small frequency $\omega .$ This implies $\mathrm{Im}\sigma \left(\omega \right)\sim D_c/\omega$ and $\mathrm{Re}\sigma \left(\omega \right)\sim D_c\tau$ for $\overrightarrow{\omega }0,$ where $D_c$ is the renormalized charge stiffness and the time $\tau$ is proportional to the strength of the impurity potential. These nontrivial effects due to forward scattering disorder are lost within the usual bosonization approach, which relies on the linearization of the energy dispersion. We discuss our result in the light of a recent experiment.

• Received 30 June 1998

DOI:https://doi.org/10.1103/PhysRevB.59.9961