Abstract:
We study the motion of a particle on the two-dimensional
honeycomb lattice whose sites are occupied by flipping rotators, which
scatter the particle according to a deterministic rule. What we find
is 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.