Multipoint local-time structure in logarithmic optical-lattice dynamics

Establish whether the multipoint structure in which normalized occupation densities at distinct fixed levels become asymptotically locked in mean square also occurs in logarithmic optical-lattice dynamics.

Background

The paper proves that, for the non-confined Feller diffusion, normalized occupation densities at distinct fixed spatial levels become asymptotically locked in mean square. This reflects a level-independent multipoint correlation structure and global spatial coherence of the local-time field.

The authors explicitly identify as unresolved whether an analogous multipoint structure appears in logarithmic optical-lattice dynamics, a related class of infinite-density systems. Resolving this question would test whether the spatial coherence found for the non-confined Feller process extends to that setting.