Ideal Resistivity in One Dimension

We analyze the ideal resistivity, $\rho$, 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, ${\Omega }_0$, with $\frac{g^2}{{\Omega }_0}$ finite, we obtain a dc resistivity $\rho \propto T^2$ instead of $T$. The result may be interpreted in terms of diffusion of electrons.