Journal of Statistical Physics

, Volume 45, Issue 3–4, pp 695–714 | Cite as

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

  • B. U. Felderhof
  • G. W. Ford


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.

Key words

One-dimensional conduction mean variance of resistance 


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Copyright information

© Plenum Publishing Corporation 1986

Authors and Affiliations

  • B. U. Felderhof
    • 1
  • G. W. Ford
    • 2
  1. 1.Institut für Theoretische Physik ARWTH AachenAachenWest Germany
  2. 2.Department of PhysicsUniversity of MichiganAnn Arbor

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