A gedankenexperiment for anomalous diffusion in a charge-fluctuating dusty plasma

Brownian motion with Gaussian-distributed step-sizes is the prototype of diffusive processes with the typical scaling of the mean-square displacement linear with time. There are, however, processes scaling slower or faster in time due to differently (e.g., power-law) distributed step-sizes, commonly referred to as sub- and superdiffusion, respectively. We address the question whether there is actually a physical reason for a discrimination between normal and anomalous diffusion or whether such processes can be regarded as a special case of normal diffusion with a complicated space- and time-dependent diffusion coefficient. In order to get to the bottom of this question, we construct a numerical gedankenexperiment, which is designed to be as simple as possible and consists of dust particles embedded as test particles into a homogeneous magnetic field that randomly changes their charge. The only parameter governing the system is the ratio of the time-scales for gyration and for recharging. By performing ful...