Multiparticle dynamics on the triangular lattice in interacting media

Abstract

We study the motion of N particles moving on a two-dimensional triangular lattice, whose sites are occupied by either left or right rotators. These rotators deterministically scatter the particles to the left (right), changing orientation from left to right (right–left) after scattering a particle. This interplay between the scatterers and the particle’s motion causes a single particle to propagate in one direction away from its initial position irrespective of the system’s configuration of scatterers, i.e. the state of the medium through which the particle moves. For multiple particles we show that the particles’ dynamics can be vastly different. Specifically, we show that a particle can become entangled with another particle potentially causing the particle’s trajectory to become periodic and that this can happen when the particles have the same or differing speeds. We describe two classes of periodic orbits based on the particles’ initial velocities. We also describe how a particle with an unbounded past trajectory implies that some, possibly other, particle(s) has an unbounded future trajectory in this and other related multiparticle models.