Localisation and interaction effects in long thin wires

The diffusion model is extended to the geometry of long thin wires. In the weak localisation limit, the author obtains the same result as that found by perturbation diagrammatic techniques. In the region where perturbation theory is not applicable, it is found that sigma varies as 1//L² when the length L of the wire is of the order of the Thouless (1977, 1980) localisation length L_c and that the AC conductivity is given by sigma varies as omega ¹//². It is suggested that transport in a long thin wire at non-zero temperatures may be dominated by a pseudo-gap which makes the conductivity rapidly vanish as T to 0. This may explain the recent data of Dean and Pepper (1983).