LOCALIZATION OF CHARGED QUANTUM PARTICLES IN A STATIC RANDOM MAGNETIC-FIELD

We consider a charged quantum particle in a random magnetic field with Gaussian, delta-correlated statistics. We show that although the single-particle properties are peculiar, two-particle quantities such as the diffusion constant can be calculated in perturbation theory. We map the problem onto a nonlinear sigma model for Q matrices of unitary symmetry with renormalized diffusion coefficient for which all states are known to be localized in d = 2 dimensions. Our results compare well with recent numerical data.