Spinless particle in a rapidly fluctuating random magnetic field

We study a two-dimensional spinless particle in a disordered Gaussian magnetic field with short-time fluctuations, by means of the evolution equation for the density matrix [x((1))\<(rho)over cap>(t)\x((2))]; in this description the two coordinates are associated with the retarded and advanced paths, respectively. In the classical limit the baricentric coordinate r =(1/2)(x((1)) + x((2))) is the particle position and the dual of the relative coordinate x = X-(1) - x((2)) its momentum. The vector potential correlator is assumed to grow with distance with a power h: when h=0 it corresponds to a delta-correlated magnetic field, when h=2 to a magnetic field with infinite range fluctuations. We fmd that the value h=2 separates two different propagation regimes, of diffusion and logarithmic growth, respectively. When h<2, r undergoes diffusion with a coefficient D-r. proportional to x(-h). AS h>2, the magnetic-field fluctuations grow with distance and D-r scales as x(-2). The width in r of the density matrix then grows for large times proportionally to ln(t/x(2)).