Ideal resistivity in one dimension

We analyze the ideal resistivity, ρ, of a one-dimensional metal at high temperatures. We have adapted a diagrammatic technique introduced by Berezinskii in the context of static disorder. Retaining the dominant vertices in the limit of vanishing electron-phonon coupling constant, g, and phonon frequency, Ω0, with g2Ω0 finite, we obtain a dc resistivity ρT2 instead of T. The result may be interpreted in terms of diffusion of electrons.