  Excitation of a model photosynthetic molecular aggregate by incoherent
sunlight is systematically examined. For a closed system, the excited state
coherence induced by the sunlight oscillates with an average amplitude that is
inversely proportional to the excitonic gap, and reaches a stationary amplitude
that depends on the temperature and coherence time of the radiation field. For
an open system, the light-induced dynamical coherence relaxes to a static
coherence determined by the non-canonical thermal distribution resulting from
the entanglement with the phonon bath. The decay of the excited state
population to the common ground state establishes a non-equilibrium
steady-state flux driven by the sunlight, and it defines a time window to
observe the transition from dynamical to static coherence. For the parameters
relevant to photosynthetic systems, the exciton dynamics initiated by the
sunlight exhibits a non-negligible amount of dynamical coherence (quantum
beats) on the sub-picosecond timescale; however, this sub-picosecond time-scale
is long enough for light-harvesting systems to establish static coherence,
which plays a crucial role in efficient energy transfer. Further, a
relationship is established between the non-equilibrium steady-state induced by
the sunlight and the coherent dynamics initiated from the ground state by a
laser $\delta$-pulse, thereby making a direct connection between incoherent
sunlight excitation and ultrafast spectroscopy.
