A schematic model discussion of the conductor to insulator transition for particle motion in a random potential

Abstract

A schematic model for the dynamics of a particle moving in a random environment is discussed where the latter is assumed to cause normal scattering and also scattering with time inversion symmetry breaking. The second mechanism changes the exponent unity to one half for the vanishing of the conductivity near the percolation threshold. It alters also the exponent of the critical conductivity spectrum from 1/2 to 1/3. The dynamics near the transition including all cross over phenomena to the usual effective medium theory results are described by a two parameter scaling law.