  Exciton transport can be enhanced in the strong coupling regime where
excitons hybridise with confined light modes to form polaritons. Because
polaritons have group velocity, their propagation should be ballistic and
long-ranged. However, experiments indicate that organic polaritons propagate in
a diffusive manner and more slowly than their group velocity. Here, we resolve
this controversy by means of molecular dynamics simulations of Rhodamine
molecules in a Fabry-P\'{e}rot cavity. Our results suggest that polariton
propagation is limited by the cavity lifetime and appears diffusive due to
reversible population transfers between polaritonic states that propagate
ballistically at their group velocity, and dark states that are stationary.
Furthermore, because long-lived dark states transiently trap the excitation,
propagation is observed on timescales beyond the intrinsic polariton lifetime.
These insights not only help to better understand and interpret experimental
observations, but also pave the way towards rational design of molecule-cavity
systems for coherent exciton transport.
