Localization of Charged Quantum Particles in a Static Random Magnetic Field

TL;DR

This paper investigates how charged quantum particles behave in a static random magnetic field, showing that while single-particle properties are unusual, two-particle diffusion can be analyzed, revealing localization in two dimensions.

Contribution

It introduces a perturbative approach to compute two-particle diffusion in a random magnetic field and maps the problem onto a non-linear sigma-model to analyze localization.

Findings

Two-particle diffusion constant can be computed perturbatively.

All states are localized in two dimensions.

Results align with recent numerical simulations.

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.