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. Our model does not contain external drive or plasma interactions that serve to drive the system away from thermodynamic equilibrium. 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 ξ(τ) on time scales τ<τ_Δ, where τ_Δ is the time at which the standard deviation σ(τ)≡⟨ξ²(τ)⟩^1/2 approaches the mean intergrain distance Δ. Others are development of humps in the distributions on multiples of Δ, anomalous Hurst exponents, and transitions from leptokurtic toward Gaussian displacement distributions on time scales τ>τ_Δ. 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. These intermittency features are quantitatively modeled by a single-particle Itô-Langevin stochastic equation with a nonlinear drift term.