TITLE: Decay Rate from the Metastable State

SPEAKER: Professor William C. Kerr,

TIME: Thursday Mar. 8, 2001 at 4 PM

PLACE: George P. Williams, Jr. Lecture Hall, (Olin 101)

The problem of nucleation theory is to calculate the rate at which a system makes a transition out of a metastable configuration, over an energy barrier, into a stable configuration. The problem is ubiquitous, appearing in scientific fields ranging from the theory of chemical reactions to phase transitions in the early Universe. The talk will start with a description of Kramers' 1940 calculation of the rate at which a single Brownian particle jumps from a metastable potential well into a stable potential well. This system illustrates the important ingredients of the problem. Then we describe our calculation of the decay rate for a continuum system. In simplest terms our system may be visualized as an elastic string lying in an asymmetric double well potential and subject to random noise forces. Calculation of the decay rate of this system leads to an interesting Schroedinger equation. The solutions of most of the solvable Schroedinger equations can be expressed in terms of hypergeometric functions, but this problem leads to a more complicated equation known as a Heun equation. After describing how to solve this equation, we will show how its solutions are used to calculate the nucleation rate for critical droplets of our model. The talk will conclude with a comparison of our calculated nucleation rates with rates obtained from computer simulations of the same system by Alford, Feldman and Gleiser.