Information theory and one-dimensional disordered conductors

Abstract

A novel method is proposed to treat the problem of the random resistance ϱ of a strictly one-dimensional conductor with static disorder. It is suggested, for the probability distribution of the transfer matrix of the conductor, the distribution of maximum information-entropy, constrained by the following physical requirements: 1) flux conservation, 2) time-reversal invariance and 3) scaling, with the length of the conductor, of the two lowest cumulants of ζ, where ϱ = sh2ζ. The preliminary results discussed in the text are in qualitative agreement with those obtained by sophisticated microscopic theories.