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Provenance of classical Hamiltonian time crystals
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  • Regular Article - Theoretical Physics
  • Open Access
  • Published: 07 August 2020

Provenance of classical Hamiltonian time crystals

  • Anton Alekseev1,
  • Jin Dai2 &
  • Antti J. Niemi2,3 

Journal of High Energy Physics volume 2020, Article number: 35 (2020) Cite this article

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A preprint version of the article is available at arXiv.

Abstract

Classical Hamiltonian systems with conserved charges and those with constraints often describe dynamics on a pre-symplectic manifold. Here we show that a pre-symplectic manifold is also the proper stage to describe autonomous energy conserving Hamiltonian time crystals. We explain how the occurrence of a time crystal relates to the wider concept of spontaneously broken symmetries; in the case of a time crystal, the symmetry breaking takes place in a dynamical context. We then analyze in detail two examples of timecrystalline Hamiltonian dynamics. The first example is a piecewise linear closed string, with dynamics determined by a Lie-Poisson bracket and Hamiltonian that relates to membrane stability. We explain how the Lie-Poisson brackets descents to a time-crystalline pre-symplectic bracket, and we show that the Hamiltonian dynamics supports two phases; in one phase we have a time crystal and in the other phase time crystals are absent. The second example is a discrete one dimensional model of a Hamiltonian chain. It is obtained by a reduction from the Q-ball Lagrangian that describes time dependent nontopological solitons. We show that a time crystal appears as a minimum energy domain wall configuration, along the chain.

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Authors and Affiliations

  1. Section of Mathematics, Université de Gèneve, 2-4 rue du Lièvre, Case postale, 64 1211, Genève 4, Switzerland

    Anton Alekseev

  2. Nordita, Stockholm University, Roslagstullsbacken 23, SE-106 91, Stockholm, Sweden

    Jin Dai & Antti J. Niemi

  3. Laboratoire de Mathematiques et Physique Theorique CNRS UMR 7350, Fédération Denis Poisson, Université de Tours, Parc de Grandmont, F37200, Tours, France

    Antti J. Niemi

Authors
  1. Anton Alekseev
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  2. Jin Dai
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Correspondence to Antti J. Niemi.

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ArXiv ePrint: 2002.07023

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Alekseev, A., Dai, J. & Niemi, A.J. Provenance of classical Hamiltonian time crystals. J. High Energ. Phys. 2020, 35 (2020). https://doi.org/10.1007/JHEP08(2020)035

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  • Received: 20 February 2020

  • Accepted: 17 July 2020

  • Published: 07 August 2020

  • DOI: https://doi.org/10.1007/JHEP08(2020)035

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Keywords

  • Differential and Algebraic Geometry
  • Field Theories in Lower Dimensions
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