  We present a rigorous theoretical description of excitonic dynamics in
molecular light-harvesting aggregates photoexcited by weak-intensity radiation
of arbitrary properties. While the interaction with light is included up to the
second order, the treatment of the excitation-environment coupling is exact and
results in an exact expression for the reduced excitonic density matrix that is
manifestly related to the spectroscopic picture of the photoexcitation process.
This expression takes fully into account the environmental reorganization
processes triggered by the two interactions with light. This is particularly
important for slow environments and/or strong excitation-environment coupling.
Within the exponential decomposition scheme, we demonstrate how our result can
be recast as the hierarchy of equations of motion (HEOM) that explicitly and
consistently includes the photoexcitation step. We analytically describe the
environmental reorganization dynamics triggered by a delta-like excitation of a
single chromophore, and demonstrate how our HEOM, in appropriate limits,
reduces to the Redfield equations comprising a pulsed photoexcitation and the
nonequilibrium Foerster theory. We also discuss the relation of our formalism
to the combined Born-Markov-HEOM approaches in the case of excitation by
thermal light.
