The wavefunction envelope in one-dimensional random potentials

Abstract

We propose a formalism for the study of mean resistance of a one dimensional chain of random potentials. We obtain the resistance as a function of the length of the chain. In the asymptotic limit, this is related to the wavefunction envelope. The formalism demands loss of translational symmetry, but is general enough to include potentials with spatial correlations which are not long ranged and also those whose randomness is inhomogeneous.