Truncated Dynamics, Ring Molecules and Mechanical Time Crystals

TL;DR

This paper explores how simplified effective theories of complex systems can exhibit novel dynamical features like time crystals, demonstrated through toy models of molecular rings and their potential physical realizations.

Contribution

It introduces the concept of truncated dynamics with unconventional Poisson brackets and proposes toy models of molecular rings where classical time crystals emerge.

Findings

Time crystals can emerge in classical effective theories of molecular rings.

Toy models demonstrate the physical plausibility of such time crystal behavior.

Potential widespread occurrence in aromatic ring molecules.

Abstract

In applications of mechanics, including quantum mechanics, we often consider complex systems, where complete solutions of the underlying "fundamental" equations is both impractical and unnecessary to describe appropriate observations accurately. For example, practical chemistry, including even precision first-principles quantum chemistry, is never concerned with the behavior of the subnuclear quarks and gluons. Instead, we often focus on a few key variables, and construct a so-called effective theory for those. Such effective theories can become complicated and non-local, even for fairly simple systems. But in many circumstances, when there is a separation of scales, we can treat the reduced set of variables as a conventional dynamical system in its own right, governed by an energy conserving Lagrangian or Hamiltonian, in a useful approximation. The structure of that emergent description can display qualitatively new features, notably including reduced dimensionality, manifested through unconventional Poisson brackets. Here we discuss the physical meaning and consequences of such truncated dynamics. We propose physically realizable toy models of molecular rings, wherein time crystals emerge at the classical level. We propose that such behavior occurs in the effective theory of highly diamagnetic aromatic ring molecules, and could be widespread.