The Effect of Noisy Magnetic Fields on Electrons

In this work, we study the behavior of an electron in the presence of a constant and uniform magnetic field, which is subjected to white noise fluctuations with an autocorrelation of magnitude Δ B . Starting from the Schwinger representation for a propagator in the presence of a constant magnetic field, we use the method of replicas to determine the effect of the magnetic noise on the shape of the renormalized quasi-particle parameters. Leading to an effective charge and an effective refraction index that depend not only on the energy scale, as usual, but also on the magnitude of the noise Δ B and the average field B.