Quantum pattern formation dynamics of photoinduced nucleation process

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.