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Provenance of classical Hamiltonian time crystals

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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Submitted on : Tuesday, March 3, 2020 - 9:56:14 PM
Last modification on : Tuesday, January 11, 2022 - 5:56:35 PM

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Anton Alekseev, Jin Dai, Antti J. Niemi. Provenance of classical Hamiltonian time crystals. Journal of High Energy Physics, Springer, 2020, 08, pp.035. ⟨10.1007/JHEP08(2020)035⟩. ⟨hal-02497870⟩

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