Critical fluctuations and anomalous transport in soft Yukawa-Langevin systems

Simulation of a Langevin-dynamics model demonstrates emergence of critical fluctuations and anomalous grain transport which have been observed in experiments on "soft" quasi-two-dimensional dusty plasma clusters. It has been suggested that these anomalies derive from particular non-equilibrium physics, but our model does not contain such physics: the grains are confined by an external potential, interact via static Yukawa forces, and are subject to stochastic heating and dissipation from neutrals. One remarkable feature is emergence of leptokurtic probability distributions of grain displacements $\xi(\tau)$ on time-scales $\tau<\tau_{\Delta}$, where $\tau_{\Delta}$ is the time at which the standard deviation $\sigma(\tau)\equiv < \xi^2(\tau) >^{1/2}$ approaches the mean inter-grain distance $\Delta$. Others are development of humps in the distributions on multiples of $\Delta$, anomalous Hurst exponents, and transitions from leptokurtic towards Gaussian displacement distributions on time scales $\tau>\tau_{\Delta}$. The latter is a signature of intermittency, here interpreted as a transition from bursty transport associated with hopping on intermediate time scales to vortical flows on longer time scales.