Symmetric Satellite Swarms and Choreographic Crystals

TL;DR

This paper introduces the concept of choreographic order as a dynamic analogue of crystalline symmetry, classifies symmetric satellite constellations, and explores potential physical systems exhibiting this novel order.

Contribution

It defines choreographic order, develops methods to classify symmetric satellite configurations, and proposes experimental signatures for detecting choreographic crystals.

Findings

Classified all symmetric satellite constellations.

Generalized to broader choreographic crystal structures.

Suggested experimental signatures for identifying choreographic order.

Abstract

In this paper, we introduce a natural dynamical analogue of crystalline order, which we call choreographic order. In an ordinary (static) crystal, a high degree of symmetry may be achieved through a careful arrangement of the fundamental repeated elements. In the dynamical analogue, a high degree of symmetry may be achieved by having the fundamental elements perform a carefully choreographed dance. For starters, we show how to construct and classify all symmetric satellite constellations. Then we explain how to generalize these ideas to construct and classify choreographic crystals more broadly. We introduce a quantity, called the "choreography" of a given configuration. We discuss the possibility that some (naturally occurring or artificial) many-body or condensed-matter systems may exhibit choreographic order, and suggest natural experimental signatures that could be used to identify and characterize such systems.