KTH/SU Mathematics Colloquium

February 11, 2009

Frank den Hollander, Leiden University and EURANDOM, The Netherlands

Metastability under stochastic dynamics

A physical, chemical or biological system driven by a noisy microscopic dynamics may explore different regions of its state space on different time scales. Indeed, for certain values of the interaction parameters controlling the microscopic dynamics, the system may move fast within a single region but move slow between different regions. The macroscopic phenomenon associated with this time scale separation is called metastability.

In this talk we consider an example from physics, namely, particles hopping on a lattice subject to on-site repulsion and off-site attraction. This system, which is referred to as the lattice gas with Kawasaki dynamics, serves as a model for condensation of a supersaturated gas. Condensation occurs only after the system manages to create a sufficiently large droplet of liquid inside the gas. The key problem is to understand the geometry of this "critical droplet" and the time the system needs to create it.

We explain what has been achieved in past years and what are the key challenges for the future.