Kramers-like 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 quasi-stationary 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.