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      Symmetric Satellite Swarms and Choreographic Crystals

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          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.

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          Most cited references 18

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          Beyond the Floquet theorem: generalized Floquet formalisms and quasienergy methods for atomic and molecular multiphoton processes in intense laser fields

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            Selection Rules for the High Harmonic Generation Spectra

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              Quantum Time Crystals

               Frank Wilczek (2012)
              Difficulties around the idea of spontaneous breaking of time translation symmetry in a closed quantum mechanical system are identified, and then overcome in a simple model. The possibility of ordering in imaginary time is also discussed.
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                Author and article information

                Journal
                2014-07-22
                2016-01-08
                Article
                10.1103/PhysRevLett.116.015503
                1407.5876

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Custom metadata
                Phys. Rev. Lett. 116, 015503 (2016)
                5 pages, 1 figure, matches version published in PRL
                cond-mat.other math-ph math.MP physics.space-ph

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