Diffusion of electrons in random magnetic fields,

TL;DR

This paper investigates how electrons diffuse in two-dimensional systems with static random magnetic fields by numerically solving the Schrödinger equation, revealing diffusive behavior and critical states away from the band edge.

Contribution

It provides a numerical analysis of electron diffusion in random magnetic fields, highlighting the diffusive growth of wave packet variance and critical states in the energy spectrum.

Findings

Wave packet variance grows diffusively away from the band edge

Auto-correlation function decay indicates fractal energy spectrum

States away from the band edge are critical

Abstract

Diffusion of electrons in a two-dimensional system in static random magnetic fields is studied by solving the time-dependent Schr\"{o}dinger equation numerically. The asymptotic behaviors of the second moment of the wave packets and the temporal auto-correlation function in such systems are investigated. It is shown that, in the region away from the band edge, the growth of the variance of the wave packets turns out to be diffusive, whereas the exponents for the power-law decay of the temporal auto- correlation function suggest a kind of fractal structure in the energy spectrum and in the wave functions. The present results are consistent with the interpretation that the states away from the band edge region are critical.