Infinite horizon Lorentz gases with static or pulsating scatterers
January 8, 2015
noon PHG 646
Abstract
The Lorentz gas consists of a point particle colliding with an extended
array of hard obstacles. It has been studied widely in statistical
mechanics and ergodic theory as a deterministic diffusion process. Recent
interest has focused on the infinite horizon case, where the scatterers are
periodic and it is possible (but of zero probability) for the particle to
avoid any collisions. In the two-dimensional static case this leads to
logarithmic superdiffusion, and anomalous convergence of the second moment
to twice the variance of the limiting normal distribution. Higher
dimensions lead to a number of interesting variations. When the scatterers
have a time-periodic radius, collisions typically increase the average
velocity of the particle. In this case heuristic arguments and numerical
simulations show that the infinite horizon enhances the acceleration,
despite longer periods without collisions.
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Last modified: April 08 2016 - 20:30:35