Droplet growth for three-dimensional Kawasaki dynamics
This paper describes metastability and nucleation for a local version of the three-dimensional lattice gas with Kawasaki dynamics. It consists in a simple exclusion where nearest-neighbors feel a binding energy that slows down dissociation and where the boundary acts as an infinite gas reservoir. For an empty initial configuration, and in a particular domain of parameters, there is a balanced competition between the two phenomena; for large \(\beta\), the system wants to fill but is slow in doing it. This paper investigates how the transition from empty to full takes place under the dynamics and identifies the critical droplet and the time of its creation in the infinite temperature limit. The work is inspired by similar studies on Glauber dynamics by Ben Arous and Cerf, but the conservative character of the dynamics requires a more delicate process and the shape of the critical droplet is e.g. more complicated. The author of this paper is focused on the geometry of the critical droplet representing the ``gate'' for the transition from the metastable to the stable set. The analysis relies on discrete isoperimetric inequality adapted from Alonso and Cerf, and the heuristics of the static and dynamic metastability are widely discussed.
scientific article; zbMATH DE number 1964636