Noisy kinks and diffusion-limited reaction
Seminar Room 1, Newton Institute
Kinks are examples of ``coherent structures'': clearly identifiable localized features in a noisy, spatially-extended system that can be followed as they move about under the influence of fluctuations. In the Phi4 stochastic partial differential equation, a steady-state mean density is dynamically maintained: kinks and antikinks are nucleated in pairs, follow Brownian paths and annihilate on meeting. Thus the kink-antikink reaction rate is controlled by collisions between diffusing particles. Classical treatment of such problems produces a hierarchy of particle correlation functions without an exact solution. However, it is possible to sidestep this hierarchy and find an exact solution for the mean number of particles per unit length as a function of time. We review an exact method for calculating the mean lifetime of a particles in a simplified model, and an exact rate equation in terms of the correlation function. In addition, the distribution of particle lifetimes is calculated under a ``constant-killing-rate'' approximation that compares favourably with the results of numerical experiments.