Localization of Charged Quantum Particles in a Static Random Magnetic Field

Abstract

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 non-linear 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.