Observation of a Trapping Transition in the Diffusion of a Thick Needle through Fixed Point Scatterers

The long-time correlation functions of an infinitesimally thin needle moving through stationary point scatterersa so-called Lorentz modelexhibits surprisingly long-time tails. These long-time tails are now seen to persist in a two-dimensional model even when the needle has a finite thickness. If the needles are too thick, then the needles are effectively trapped at all nontrivial densities of the scatterers. At needle widths approximately equal to or smaller than σ = ε/20 where ε is the average spacing between scatterers, the needle diffuses and exhibits the crossover transition from the expected Enskog behavior to the enhanced translation diffusion seen earlier by Höfling, Frey and Franosch [ Phys. Rev. Lett. 2008, 101, 120605 ]. At this needle width, an increase in its center-of-mass diffusion with respect to increasing density is seen after a crossover density of n* ≈ 5 is reached. (The reduced density n* is defined as n* = n L 2 where n is the number density of particles and L is the needle length.) The crossover transition for needles with finite thickness is spread over a range of densities exhibiting intermediate behavior. The asymptotic divergence of the center of mass diffusion is suppressed compared to that of infinitely thin needles. Finally, a new diminished diffusion regime, apparently due to the increased importance of head-on collisions, now appears at high scattering densities.