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))]; i n this description the two coordinates are associated with the retarde d and advanced paths, respectively. In the classical limit the baricen tric 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 fiel d, when h=2 to a magnetic held with infinite range fluctuations. We fm d that the value h=2 separates two different propagation regimes, of d iffusion and logarithmic growth, respectively. When h<2, r undergoes d iffusion with a coefficient D-r. proportional to x(-h). AS h>2, the ma gnetic-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 propor tionally to ln(t/x(2)).