Information theory and resistance fluctuations in one-dimensional disordered conductors

Abstract

A novel method is proposed to treat the problem of the random resistance of a strictly one-dimensional conductor with static disorder. For the probability distribution of the transfer matrix R of the conductor we propose a 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 ω, where R=exp(iω→·Jbhat). The preliminary results discussed in the text are in qualitative agreement with those obtained by sophisticated microscopic theories.