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 ρ∝T² instead of T. The result may be interpreted in terms of diffusion of electrons.