# Multiparticle Dynamics on the Triangular Lattice in Interacting Media

## TL;DR

This paper investigates the complex dynamics of multiple particles moving on a triangular lattice with scatterers, revealing how interactions can lead to periodic trajectories and unbounded motion, highlighting the rich behavior in multiparticle systems.

## Contribution

It introduces a detailed analysis of multiparticle interactions on a triangular lattice with rotator scatterers, identifying conditions for periodic and unbounded trajectories, a novel insight into such deterministic models.

## Key findings

- Particles can become entangled, leading to periodic orbits.
- Multiple particles exhibit a range of behaviors from bounded to unbounded trajectories.
- The initial velocities influence the emergence of periodic or unbounded motion.

## 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 to 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. 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.