What's the difference between a time crystal and a system undergoing periodic motion? My understanding of a crystal is that it is a rigid body with a spatially periodic structure. Is any system undergoing periodic motion a time crystal, or is there some other requirement that makes it special? In other words, what (if anything) excludes the ideal simple harmonic oscillator from the category of time crystal?


1 Answer 1


A crystal is a system which spontaneously breaks the translation symmetry of the underlying physical laws.

Similarly, a time crystal is a system which is subject to a periodic driving with period $T$, but which however does not oscillate with the same period but shows oscillations which a different period $T'=kT$ with $k>1$ integer, i.e., which spontaneously breaks the (discrete) time translation symmetry.

This answer provides a very nice explanation of time crystals.

  • 1
    $\begingroup$ Naive (and redundant) question but just to confirm, a system with time-independent Hamiltonian that shows oscillations with some time-period $T>0$ still won't be a time-crystal as long as there is no spontaneous symmetry breaking of time-translational symmetry, right? $\endgroup$
    – ACat
    Aug 22, 2021 at 16:28

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.