Fractional Laplacian Spectral Approach to Anomalous Diffusion in Dusty Plasma

From transport of energetic particles in the solar corona to the spread of pollutants in the Earth’s atmosphere, anomalous diffusion processes are ubiquitous in natural systems. The physical origins of such processes and their effect on global system stability present important open questions in non-equilibrium statistical mechanics. Here we discuss anomalous diffusion of dust particles in complex plasma monolayers on Earth and filamentary structures in microgravity. Specifically, we demonstrate that the associated dust velocity histograms are non-Maxwellian and the time evolution of mean squared displacement deviates from linear. We argue that at critical scales within the system, anomalous dust diffusion, guided by nonlocal interactions, leads to enhancement of energy transport and increased probability for excitation of instabilities.