Conductivity of One-Dimensional Interacting Fermions

Using an exactly soluble model, the decay rate of a current-carrying state of one-dimensional fermions is calculated in the presence of random scatterers at finite temperature and the dc conductivity thereby inferred. For interacting fermions it is modified by a factor ${(\frac{T}{T}+\theta )}^g$, where $g$ is a positive (negative) coupling constant for repulsive (attractive) two-body forces. While the conductivity could be greatly enhanced for $g<\mathrm{}0\mathrm{}$ and $T\ll \theta$, one-dimensional superconductivity appears ruled out at any finite temperature.