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.