  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 $<x^{(1)} |\hat{\rho} (t)| x^{(2)}>$; in this
description the two coordinates are associated with the retarded and advanced
paths respectively. The static part of the vector potential correlator is
assumed to grow with distance with a power $h$; the case $h = 0$ corresponds to
a $\delta$-correlated magnetic field, and $h = 2$ to free massless field. The
value $h = 2$ separates two different regimes, diffusion and logarithmic growth
respectively. When $h < 2$ the baricentric coordinate $r = (1/2)(x^{(1)} +
x^{(2)})$ diffuses with a coefficient $D_{r}$ proportional to $x^{-h}$, where
$x$ is the relative coordinate: $x = x^{(1)} - x^{(2)}$. As $h > 2$ the
correlator of the magnetic field is a power of distance with positive exponent;
then the coefficient $D_{r}$ scales as $x^{-2}$.
  The density matrix is a function of $r$ and $x^2/t$,and its width in $r$
grows for large times proportionally to $log(t/x^2)$.
