Classical dynamics in a random magnetic field

The classical dynamics in a quenched random magnetic field is investigated using both the Langevin and Boltzmann equations. In the former case, a field-theoretic method permits the average over the random magnetic field to be performed exactly. A self-consistent theory is constructed using the functional method for the effective action, allowing a determination of the particle response to external forces. In the Boltzmann approach the random magnetic field is treated as a random Lorentz driving force, Langevin dynamics always leads to negative magnetoresistance, whereas the Boltzmann description can lead to either positive or negative magnetoresistance. In both descriptions the resistivity decreases at low average magnetic fields as the temperature increases. In contrast to the Langevin result, the Boltzmann resistivity increases at moderate fields as a function of temperature, displaying a nonmonotonic temperature dependence. The transverse resistivity decreases as the temperature increases in the case of Langevin dynamics, whereas the opposite behavior occurs in the Boltzmann case.