  We study the dynamics of quantum pattern formation processes in molecular
crystals which is a concomitant with photoinduced nucleation. Since the
nucleation process in coherent regime is driven by the nonadiabatic transition
in each molecule followed by the propagation of phonons, it is necessary to
take into account the quantum nature of both electrons and phonons in order to
pursue the dynamics of the system. Therefore, we employ a model of localized
electrons coupled with a quantized phonon mode and solved the time-dependent
Schr\"odinger equation numerically. We found that there is a minimal size of
clusters of excited molecules which triggers the photoinduced nucleation
process, i.e., nucleation does not take place unless sufficient photoexcitation
energy is concentrated within a narrow area of the system. We show that this
result means that the spatial distribution of photoexcited molecules plays an
important role in the nonlinearity of the dynamics and also of the optical
properties observed in experiments. We calculated the conversion ratio, the
nucleation rate, and correlation functions to reveal the dynamical properties
of the pattern formation process, and the initial dynamics of the photoinduced
structural change is discussed from the viewpoint of pattern formation.
