LOCALIZATION IN A RANDOM MAGNETIC-FIELD - THE SEMICLASSICAL LIMIT

We study the two-dimensional electron gas in the presence of a random perpendicular magnetic field. We examine, in particular, the limit in which the correlation length of the random field is large compared to the typical magnetic length. In this limit, a semiclassical approach c an be used to understand a large part of the energy spectrum. To inves tigate localization, we introduce a simplified model, in which electro ns propagate coherently on a random network derived from the classical trajectories. The same network model (with different parameters) also represents electron motion in a uniform magnetic field and a random s calar potential, in a spin-degnerate Landau level. Requiring that the global phase diagram of our model be consistent with Khmelnitskii's sc aling flow for the quantum Hall effect, we argue that all electron sta tes in a random magnetic field are localized in the semiclassical limi t. We present the results of numerical simulations of the model in sup port of this conclusion.