Classical Fractons: Local chaos, global broken ergodicity and an arrow of time

TL;DR

This paper explores classical fractons, revealing that while they break global ergodicity, local clusters can exhibit limited ergodic or chaotic behavior, and their dynamics feature a central Janus point indicating a bidirectional arrow of time.

Contribution

It demonstrates that classical fractons can have locally ergodic or chaotic clusters and introduces the concept of a Janus point as a universal feature of their dynamics.

Findings

Clusters can exhibit ergodic or chaotic behavior depending on the Hamiltonian.

Fracton trajectories often have a central Janus point.

Global ergodicity is broken, but local ergodic behavior persists within clusters.

Abstract

We report new results on classical nonrelativistic dipole conserving particles - fractons. These have been previously shown to exhibit "Machian" dynamics where the motion of one particle requires the presence of others in its proximity, such that dynamics produces ergodicity breaking steady states characterized by clusters. In this work, we show that although the global state breaks ergodicity, a limited version of ergodic behavior is retained within the clusters which may or may not be chaotic, depending on the nature of the microscopic Hamiltonian. In certain cases, we show that the dynamics can be mapped to that of a billiards particle in various stadiums. We also show that the many-fracton trajectories characteristically exhibit a central time or "Janus point" and thus a generic nonequilibrium bidirectional arrow of time.