Can short-range open quantum systems host stable continuous time crystals
In plain words
Some pumped, leaky systems oscillate forever on their own, breaking time-translation symmetry without a periodic drive. Known examples rely on every atom coupling to every other, and it is unknown whether short-range systems can do this.
Precise statement
For Lindblad dynamics with a time-independent generator and finite-range interactions on a d-dimensional lattice, does a phase exist in which local observables oscillate persistently (a limit cycle) with period independent of initial conditions and coherence time diverging with system size? Boundary time crystals (Iemini et al. 2018) achieve this with collective all-to-all coupling. Answer yes or no as a function of d.
What would settle it
A finite-range model with field-theory and numerical evidence that oscillation coherence time diverges with system size, or an argument excluding it for all d.
Status in the literature
A continuous time crystal was observed in 2022 in an atom-cavity system with global coupling (Kongkhambut et al., Science).