  Excited state carriers, such as excitons, can diffuse on the 100 nm to micron
length scale in molecular materials, but they only delocalize over short length
scales due to coupling between electronic and vibrational degrees-of-freedom.
Here, we leverage the locality of excitons to adaptively solve the hierarchy of
pure states equations (HOPS). We demonstrate that our adaptive HOPS (adHOPS)
methodology provides a formally exact and size-invariant (i.e. O(1)) scaling
algorithm for simulating mesoscale quantum dynamics. We provide
proof-of-principle calculations for exciton diffusion on linear chains
containing up to 1000 molecules.
