Colloidal statistical mechanics in optical vortices

Colloidal particles driven by an optical vortex constitute a model driven-dissipative system in which both macroscopic and microscopic aspects of transport can be studied. We find that the single-particle diffusion in an optical vortex can be either normal super-diffusive or sub-diffusive depending on the number of particles in the vortex and on the timescale over which the diffusion is measured. For a three particle system we find that the particles dynamics can be either steady-state periodic or with weakly chaotic characteristics depending on the relative effect of modulations in the intensity along the vortex and hydrodynamic interactions between the spheres, We introduce the use of the N-fold bond orientational order parameter to characterize particle circulating in a ring by one macroscopic quantity, for a three particle system we show that for short time scales the single-particle super-diffusion corresponds to a super-diffusive motion of the order parameter, At longer time scales we find that the order parameter asymptotes to the expected normal diffusion behavior for the steady state system, while fractional dynamics develop in the weakly chaotic system. Moreover, we confirm a prediction that related the power laws governing the fractional dynamics with those governing the weakly chaotic behavior.