Time crystals: a review. (arXiv:1704.03735v5 [quant-ph] UPDATED)

Time crystals are time-periodic self-organized structures postulated by Frank
Wilczek in 2012. While the original concept was strongly criticized, it
stimulated at the same time an intensive research leading to propositions and
experimental verifications of discrete (or Floquet) time crystals -- the
structures that appear in the time domain due to spontaneous breaking of
discrete time translation symmetry. The struggle to observe discrete time
crystals is reviewed here together with propositions that generalize this
concept introducing condensed matter like physics in the time domain. We shall
also revisit the original Wilczek's idea and review strategies aimed at
spontaneous breaking of continuous time translation symmetry.

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