Classical Time Crystals

TL;DR

This paper explores the concept of classical time crystals, demonstrating that certain classical systems can exhibit stable, lowest-energy periodic motion, akin to spatial crystals, challenging previous assumptions.

Contribution

It introduces models of classical time crystals, showing that systems can have lowest-energy states with nontrivial periodic motion, overcoming prior challenges.

Findings

Classical systems can exhibit stable, lowest-energy periodic orbits.

Models with traveling density waves demonstrate time crystalline behavior.

Theoretical framework for classical time crystals is established.

Abstract

We consider the possibility that classical dynamical systems display motion in their lowest energy state, forming a time analogue of crystalline spatial order. Challenges facing that idea are identified and overcome. We display arbitrary orbits of an angular variable as lowest-energy trajectories for nonsingular Lagrangian systems. Dynamics within orbits of broken symmetry provide a natural arena for formation of time crystals. We exhibit models of that kind, including a model with traveling density waves.