Regularizations of Time Crystal Dynamics

TL;DR

This paper shows how non-convex Lagrangians in time crystal theories can be realized in real systems, resolving singularities and revealing microstructures like Sisyphus dynamics, which become regular in quantum mechanics.

Contribution

It introduces a physical realization of non-convex Lagrangians in time crystals and explains how dynamical singularities are resolved through microstructure.

Findings

Non-convex Lagrangians can describe real systems.

Dynamical singularities are resolved by microstructure.

Quantum effects can smooth out microstructure.

Abstract

We demonstrate that non-convex Lagrangians, as contemplated in the theory of time crystals, can arise in the effective description of conventional, physically realizable systems. Such embeddings resolve dynamical singularities which arise in the reduced description. Microstructure featuring intervals of fixed velocity interrupted by quick resets - ``Sisyphus dynamics'' - is a generic consequence. In quantum mechanics this microstructure can be blurred, leaving entirely regular behavior.