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I What is a "Space-Time Crystal"?

  1. Sep 19, 2016 #1
    I know what the definition is, but the concept it's conjuring for me seems in my experience of learning about these things, to indicate that I'm missing the point completely. What does it mean for something to be oscillating when it's in a ground state? I was under the impression that such a thing is impossible unless there's some external thermodynamic input. Is this a hypothetical structure that is believed *not* to exist, but is interesting as a thought experiment?

    Naively it sounds like a PPM, which is why I assume that I must be missing quite a bit.
  2. jcsd
  3. Sep 20, 2016 #2


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    I just read the presentation by Wilczek cited in Wikipedia:

    A general feature of broken symmetry states (which Wilczek doens't mention) is that the generator of the broken symmetry - i.e. the Hamiltonian in our case -
    can't be represented as an operator in the Hilbert space any more. For infinite systems, whether time translation symmetry is broken or not, this is the generic case. E.g. a gas of atoms of which a given fraction is in an excited state has infinite energy relative to the ground state. Hence the hamiltonian is not a well defined operator.
    So we can't rely on any proof that the hamiltonian has only non-degenerate ground states simply because the Hamiltonian does not exist.

    Edit: I just found this article which elaborates on the comment I made:
    Last edited: Sep 20, 2016
  4. Sep 20, 2016 #3
    Thanks for the explanation, and the links!
  5. Mar 9, 2017 #4


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    Last edited by a moderator: May 8, 2017
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