[Pyxl101]

> In terms of frequencies, if the drive frequency is f = 1/T, then this system responds at a frequency f/2, whereas normal systems can only respond at frequencies f, 2f, 3f, ... that correspond to harmonics.

Interesting. I heard it described once that a particle with spin of 1/2 is like a particle that you have to rotate twice (through two 360 degree rotations) before it's in the same configuration. Wikipedia actually has a visualization that seems to depict this reasonably: https://en.wikipedia.org/wiki/Spin-%C2%BD

Anyway, your description makes it sound like this system by responding at f/2 might have an analogous property with time. Is this at all a reasonable or correct analogy?

[cortiver]

This is a great question. (I am the first author on the "Floquet time crystals" paper referred to btw). The analogy is not perfect because what actually happens to a spin-1/2 particle under a 360 degree rotation is it comes back to the same configuration, but its wavefunction picks up a quantum phase factor of (-1), which is not observable. On the other hand, a Floquet time crystal does actually does go to an observably different state under a time shift. The best analogy is really to, for example, a magnet, which does go to an observably different state if you rotate it (because the north and south poles rotate).

[selimthegrim]

The appendix relates this +/1 (Z2) phase factor to the so called "cat states" of the spin system. There are deeper ways to understand its more general consequences through a type of math called cohomology theory but it's not possible to make general statements about time per se. Now, if you're interested in how information moves in spin systems with respect to time I urge you to explore the fascinating topic of Lieb-Robinson bounds, but I feel like this overview might boil down for you what the paper is trying to accomplish more idiomatically: http://www.condmatjournalclub.org/jccm-content/uploads/2016/...