Growth of resistance with density of scatterers in one dimensional wave propagation

Abstract

We study wave propagation in a one-dimensional disordered array of scattering potentials. We consider three different ensembles of scatterer configurations: anN-ensemble with a fixed numberN of scatterers, anL-ensemble with a varying number of scatterers distributed over a fixed lengthL, and anNL-ensemble where bothN andL are fixed. The latter ensemble allows a detailed study of the mean resistance and its variance for a fixed lengthL as the number of scatterersN increases. We find that the Landauer result, which predicts an exponential increase of the mean resistance withN, is valid only in the low-density regime. At high density the mean resistance grows exponentially with √N and the concept of optical potential applies. In the crossover regime we find an interesting resonance.