Localization of charged quantum particles in a static random magnetic field

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Abstract
We consider a charged quantum particle in a random magnetic field with Gaussian, δ-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 σ 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.
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