Kramers-type picture for crystal nucleation

Abstract

We introduce a new scheme to analyze the kinetics of homogeneous nucleation in terms of a global order parameter. Our approach is based on the application of the internal degrees of freedom formalism to derive a kinetic equation of the Kramers type formulated for a global reaction coordinate. We provide explicit expressions for the quantities and coefficients involved in the process, suitable for simulation. In addition, our picture recovers in the quasistationary case the transition rate obtained from the method of reactive flux. The equation we present may provide a link between theoretical approaches to homogeneous nucleation (generally formulated in terms of a kinetic equation of the Fokker–Planck type) and simulations (which mostly employ linear response theory). In this context, our scheme provides a theoretical framework to interpret and extend the results obtained in recent simulations.