  Understanding the pathways taken by a quantum particle during a transport
process is an enormous challenge. There are broadly two different aspects of
the problem that affect the route taken. First is obviously the couplings
between the various sites, which translates into the intrinsic "strength" of a
state-to-state channel. Apart from the inter-state couplings, the solvents
affecting the energies of the state, and their relative coupling strengths and
time-scales form the second factor. This impact of dissipative media is
significantly more difficult to analyze. Building on recently derived relations
between coherences and population derivatives, we present an analysis of the
transport that allows us to account for both the effects in a rigorous manner.
We demonstrate the richness hidden behind the transport even for a relatively
simple system, a 4-site coarse-grained model of the Fenna-Matthews-Olson
complex. The effect of the local dissipative media is highly non-trivial. We
show that while the impact on the total site population may be small, there are
dramatic changes to the pathway taken by the transport process. The ability to
untangle the dynamics at a greater granularity opens up possibilities in terms
of design of novel systems with an eye towards quantum control.
