On the dynamics of fluctuations in time crystals

TL;DR

This paper analyzes the behavior of quantum fluctuations in time crystals, revealing their classification into phonon-like modes and exploring their decay, interactions, and potential experimental signatures.

Contribution

It introduces an effective field theory framework for fluctuations in time crystals, identifying phonon-like modes and their properties, which is a novel approach in the study of these systems.

Findings

Fluctuations in time crystals resemble acoustic and optical phonons.

Goldstone modes are gapless and relate to broken time translation symmetry.

Gapped optical modes interact and decay in characteristic ways.

Abstract

We study the evolution of quantum fluctuations in systems known as time crystals, hypothetical systems for which the lowest energy state performs a periodic motion. We first discuss some general properties shared by time crystals, and deduce the effective field theory parametrizing the evolution of their fluctuations. We show that these fluctuations fall into categories analogous to acoustic and optical phonons, encountered in conventional crystals. The acoustic phonons correspond to gapless Goldstone boson modes parametrizing the broken time translation invariance of the crystal, whereas the optical phonons are identified with modes perpendicular to the broken symmetry of the system, which generically remain gapped. We study how these two modes decay and interact together, and discuss some observable features that could be tested in experimental realizations of time crystals.