Self-Avoiding Modes of Motion in a Deterministic Lorentz Lattice Gas

Math Physics Seminar
Friday, October 16, 2015 - 2:00pm
1 hour (actually 50 minutes)
Skiles 006
Brigham Young University
We consider the motion of a particle on the two-dimensional hexagonal lattice whose sites are occupied by flipping rotators, which scatter the particle according to a deterministic rule. We find that the particle's trajectory is a self-avoiding walk between returns to its initial position. We show that this behavior is a consequence of the deterministic scattering rule and the particular class of initial scatterer configurations we consider. Since self-avoiding walks are one of the main tools used to model the growth of crystals and polymers, the particle's motion in this class of systems is potentially important for the study of these processes.