Possible Long Time Tails in Current-Current Correlation Function for Two-Dimensional Electron Gas in Random Magnetic Field

We consider a two-dimensional degenerate electron gas in the presence of perpendicular random magnetic field. The magnetic field disorder which is assumed to be Gaussian is characterized by two parameters. The first is proportional to the amplitude of local magnetic field fluctuations. The second one characterizes the disorder on the longer scale - we call it the screening length. Using the Kubo formula for the conductivity we have found a class of diagrams which leads to the long time tails in the current-current correlation function. For short times in comparison with the diffusion time corresponding to the screening length this function behaves like logarithm of time, for longer times it decays like t$\text{}^{-1}$ which of course brings into question the diffusive character of the behavior of the charged particle in random magnetic field widely assumed in the literature.