Macroscopic approach to universal conductance fluctuations in disordered metals

Abstract

Recently, a macroscopic theory of N-channel disordered condeuctors showed that the statistical distribution of the transfer matrix for a system of length L evolves with L according to a diffusion equation in N dimensions. It is proved here that the recently observed universal conductance fluctuations in normal metals at very low temperatures are a rigorous consequence of that diffusion equation, in the regime in which L≫ (mean free path) and N≫1. The value found for the fluctuation coincides with the one obtained from elaborate microscopic calculations.