It is a given that at room temperature there is plenty of perpetual chaotic and truly perpetual motion to be had. And sometimes this motion takes on some more organized forms as is the case with Nitrogen inversion.
Also it is well established that unexpected movements can occur close to absolute zero, when for instance superfluid liquids climb up the walls of their containment.
In general, unperturbed quantum systems develop in a unitary manner (i.e. a kind of movement) and will do so perpetually, until measured.
In case of super-sized Rydberg atoms you can also approach an almost classical orbit (and that should hold at very low temperatures as well). But to have sustained, detectable perpetual motion in the ground state of a system at absolute zero would be a new quality.
“I was thinking about the classification of crystals, and then it just occurred to me that it’s natural to think about space and time together, (…) So if you think about crystals in space, it’s very natural also to think about the classification of crystalline behavior in time.”
It’ll be up to some creative experimentalist to determine if the resulting theory holds water. If so, this may open up an interesting new venue to tackle the frustrating problem of getting General Relativity (where space and time is a combined entity) and QM to play together.