  Using renormalization group methods, we develop a rigorous coarse-grained
representation of the dissipative dynamics of quantum excitations propagating
inside open macromolecular systems. We show that, at very low spatial
resolution, this quantum transport theory reduces to a modified Brownian
process, in which quantum delocalization effects are accounted for by means of
an effective term in the Onsager-Machlup functional. Using this formulation, we
derive a simple analytic solution for the time-dependent probability of
observing the quantum excitation at a given point in the macromolecule. This
formula can be used to predict the migration of natural or charged quantum
excitations in a variety of molecular systems including biological and organic
polymers, organic crystalline transistors or photosynthetic complexes. For
illustration purpose, we apply this method to investigate intelastic electornic
hole transport in a long homo-DNA chain.
