Adiabatic and irreversible classical discrete time crystals

TL;DR

This paper demonstrates the simulation of classical discrete time crystals formed by colloidal particles responding adiabatically to a periodically changing magnetic field, revealing topological effects and phase transitions.

Contribution

It introduces a novel simulation of adiabatic and irreversible classical discrete time crystals with topological properties and many-body effects.

Findings

Adiabatic time crystals occur at low frequencies due to topology.

Coupling induces topologically isolated time crystals.

Dynamical phase transitions between different space-time arrangements.

Abstract

We simulate the dynamics of paramagnetic colloidal particles that are placed above a magnetic hexagonal pattern and exposed to an external field periodically changing its direction along a control loop. The conformation of three colloidal particles above one unit cell adiabatically responds with half the frequency of the external field creating a time crystal at arbitrary low frequency. The adiabatic time crystal occurs because of the non-trivial topology of the stationary manifold. When coupling colloidal particles in different unit cells, many body effects cause the formation of topologically isolated time crystals and dynamical phase transitions between different adiabatic reversible and non-adiabatic irreversible space-time-crystallographic arrangements.