Abstracts:

Francesca Nardi

Droplet growth for three-dimensional Kawasaki dynamics.

The goal of this paper is to describe metastability and nucleation for a local version of the three-dimensional lattice gas with Kawasaki dynamics at low temperature and low density.

Let L subset of $Z^3$ be a large finite box. Particles perform simple exclusion on L, but when they occupy neighboring sites they feel a binding energy -U<0 that slows down their dissociation. Along each bond touching the boundary of L from the outside, particles are created with rate r=exp(-D/T) and are annihilated with rate 1, where 1/T is the inverse temperature and D>0 is an activity parameter. Thus, the boundary of L plays the role of an infinite gas reservoir with density r.

We consider the regime where D in (U,3U) and the initial configuration is such that L is empty. For large 1/T, the system wants to fill L but is slow in doing so. We investigate how the transition from empty to full takes place under the dynamics. In particular, we identify the size and shape of the it critical droplet and the time of its creation in the limit as 1/T to infinity.

Andre Verbeure

 Bose-Einstein Condensation (BEC)

Since three quarters of a century the phenomenon of BEC is theoretically predicted for free Bosons. This means that the phenomenon is a pure quantum effect!. Experimentally it is believed that BEC is the basis of e.g. superfluidity. The experiments of 1995 with trapped bosons changed the world of BEC physics as well for experimentalists as for theoreticians.
BEC is directly measured. For theoreticians the old challenge to prove that BEC persists with interactions is again at order. In the lecture the problem is presented in a mathematically rigorous way and a proof of BEC is explained for a class of interacting boson systems.
The content of the lecture contains:
- BEC for the ideal bose gas
- BEC in the van der Waals limit
- BEC for an interacting boson system
- BEC for trapped bosons