WAVE-PROPAGATION IN ONE-DIMENSIONAL DISORDERED STRUCTURES

Wave propagation in one-dimensional disordered structures is studied via a variable R, which represents the quantum-mechanical resistance to electronic transport, or the ratio of total-energy density to power flux for electromagnetic propagation. R is formulated by three distinct methods: (1) differential equation, (2) perturbation series, (3) state-variable representation. An explicit solution for R is obtained in the limit of small fluctuations of the potential (or dielectric constant). The configurational-average state vector is determined in the second cumulant approximation for stationary processes, and an explicit expression is given for the average [R] for any potential distribution. The electron localization length exhibits a minimum as a function of the correlation length of the random potential. The exact expression for [R] is obtained for a white-noise distribution of potentials (or dielectric constants), both from the perturbation series, and from the state-variable formulation.