Katie Newhall

Energy landscapes, metastability, and transition paths

The classic example of metastability (infrequent jumps between deterministically-stable states) arises in noisy systems when the thermal energy is small relative to the energy barrier separating two states. The most probable path the system follows during such a transition is everywhere parallel to the gradient of the system. I will present three extensions of these ideas. The first is an infinite-dimensional system for which I prove metastability is present in the absence of an energy barrier; I extend transition state theory to compute mean transition times. In the second, I derive a model for a spatially-extended magnetic system with spatially-correlated noise designed to sample the Gibbs distribution relative to a defined energy functional. In the third, I show a quasi-potential can be found and used to describe metastable transitions between stable clusters in a bead-spring polymer model of chromosome dynamics with additional stochastic binding pushing the system out of equilibrium.