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The key idea is that time crystals are externally driven at a certain frequency, but they respond at a different (in fact, slower) frequency. First of all, terminology: what does it have in common with the usual concept of crystals, whose whole structure can be represented by spatially replicating the unit cell. Is the time crystal an addendum to the ...


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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 ...


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This is a review article on the status of the research by summer of 2017. I copy the conclusions: In the present article we have reviewed current state of the art of investigations of time crystals originally pro- posed by Wilczek (Wilczek, 2012), i.e. the phenomena that are related to self-organization of quantum many- body systems in time. This ...


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A flaw in Wilczek's argument has been pointed out in PRL 110, 118901 (2013). In short, the rotating soliton exhibited by Wilczek is not the correct ground state of the system. The true ground state can be shown to be stationary, irrespective of the flux. Impossibility of a quantum system with time-crystal-like ground-state has been further addressed in PRL ...


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Let me try to explain with an example. Let's consider for instance the honeycomb lattice shown below. What type of lattice is this? Now since this is a two dimensional structure, we might expect that we are able to identify all the points with a linear combination of two vectors $\bf{a}_1$ and $\bf{a}_2$: $n\bf{a}_1 + m\bf{a}_2$, where the coefficients $m,n$ ...


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If you consult the September, 2018, issue of Physics Today you will find an excellent article on time crystals by N Yao and C Nayak (p 41). Paraphrasing their synopsis, time crystals result when the discrete time translation symmetry of isolated periodically driven systems is spontaneously broken. They are a quantum manifestation of the complex behavior of ...


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I am going to make this brief. As pointed out space has a crystalline structure in LQG. This has some odd problems in that it violates Lorentz invariance on scales close to the scale length of the crystal. It also has to be remembered that spacetime is transformed by Lorentz boosts, so a crystalline structure in one frame involves a different spatial surface ...


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It depends entirely on your exact definitions. Many times, someone has proposed a "classical time crystal", but then someone else has argued that that isn't a "true" time crystal because it's time crystality doesn't originate from the quantum effects that the latter person thinks make the effect really interesting. Some people consider that to be a "no true ...


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A quantum time crystal does not from my reading of Wilczek and others appear to require entanglement, but the idea is interesting. It does seems plausible that a quantum time crystal model could be developed with entanglement. A quantum time crystal is just a periodicity in a system in time that has a lattice structure. An elementary quantum time crystal is ...


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