A. Bovier (WIAS), F. den Hollander (EURANDOM), F. Nardi (Roma 1)
Sharp asymptotics for Kawasaki dynamics
on a finite box with open boundary
(1011K, PS)
ABSTRACT. In this paper we study the metastable behavior of the lattice gas in two
and three dimensions subject to Kawasaki dynamics in the limit of low
temperature and low density. We consider the local version of the model,
where particles live on a finite box and are created, respectively,
annihilated at the boundary of the box in a way that reflects an
infinite gas reservoir. We are interested in how the system nucleates,
i.e., how it reaches a full box when it starts from an empty box. Our
approach combines geometric and potential theoretic arguments.
In two dimensions, we identify the full geometry of the set of critical
droplets for the nucleation, compute the average nucleation time up to a
multiplicative factor that tends to one in the limit of low temperature and
low density, express the proportionality constant in terms of certain
capacities associated with simple random walk, and compute the asymptotic
behavior of this constant as the system size tends to infinity. In three
dimensions, we obtain similar results but with less control over the geometry
and the constant.
A special feature of Kawasaki dynamics is that in the metastable regime
particles move along the border of a droplet more rapidly than they arrive
from the boundary of the box. The geometry of the critical droplet and the
sharp asymptotics for the average nucleation time are highly sensitive to
this motion.