Coulomb-gas approach to quantum motion in random magnetic fields

We study the motion in the plane of a spinless particle subject to a random magnetic field, in terms of Feynman’s influence functional. We show that with δ-correlated fields the Gaussian regime is dominated by one-dimensional quantum motion over classical walks. In the case of long-range field correlations the system is described as a two-dimensional Coulomb gas, where the plasma phase is dominated by free-particle propagation and the low-temperature phase by a regime of strong coupling between advanced and retarded paths. The semiclassical regime is also discussed.