  Coherent dynamics of coupled molecules are effectively characterized by the
two-dimensional (2D) electronic coherent spectroscopy. Depending on the
coupling between electronic and vibrational states, oscillating signals of
purely electronic, purely vibrational or mixed origin can be observed. Even in
the "mixed" molecular systems two types of coherent beats having either
electronic or vibrational character can be distinguished by analyzing
oscillation Fourier maps, constructed from time-resolved 2D spectra. The
amplitude of the beatings with the electronic character is heavily affected by
the energetic disorder and consequently electronic coherences are quickly
dephased. Beatings with the vibrational character depend weakly on the
disorder, assuring their long-time survival. We show that detailed modeling of
2D spectroscopy signals of molecular aggregates providesdirect information on
the origin of the coherent beatings.
