TITLE: Nucleation Rates in an Extended System with an Asymmetric Local Potential

SPEAKER: Andrew J. Graham,

We have calculated the rate for thermal decay from the metastable state for a spatially extended 1-d system with an asymmetric double-well local potential. The calculation is based on the formalisms developed by Langer [J. S. Langer, Ann. Phys. (N.Y.) 54, 258 (1969)] and by Buettiker and Landauer [M. Buettiker and R. Landauer, Phys. Rev. A 23, 1397 (1981)]. The ingredients of our calculation are an analytical solution for the saddle point in phase space and an evaluation of the spectrum of small oscillations around that saddle point. We find that the eigenvalue equation for the small oscillation spectrum reduces to a Heun equation, a generalization of the hypergeometric equation that has four regular singular points. We obtain a solution of the (functional) Fokker-Planck equation in the full phase space of the system. Our results compare favorably with results published from computer simulations on the same system [M. Alford, H. Feldman and M. Gleiser, Phys. Rev. D 47, R2168 (1993)].