Appearance of a homochiral state of crystals induced by random fluctuation in grinding.

We study crystallization of chiral crystals from achiral molecules using a master equation based on a simple reaction model. Although there is no chiral symmetry breaking in the reaction model, random fluctuations drive the system to a homochiral state. The time necessary for the appearance of the homochiral state is proportional to the total number of molecules in the system. This behavior is described by a diffusion equation in a size space with a position-dependent diffusion coefficient. We also study the effect of chiral impurities, which affect the crystal growth. Depending on the type of impurities, the chiral symmetry breaking occurs either deterministically or with the help of random fluctuations.