  We consider a molecular aggregate consisting of $N$ identical monomers. Each
monomer comprises two electronic levels and a single harmonic mode. The
monomers interact with each other via dipole-dipole forces. The monomer
vibrational modes are bilinearly coupled to a bath of harmonic oscillators.
This is a prototypical model for the description of coherent exciton transport,
from quantum dots to photosynthetic antennae. We derive an exact quantum master
equation for such systems. Computationally, the master equation may be useful
for the testing of various approximations employed in theories of quantum
transport. Physically, it offers a plausible explanation of the origins of
long-lived coherent optical responses of molecular aggregates in dissipative
environments.
