How an Anomalous Cusp Bifurcates

Abstract

We study the pattern of activated trajectories in a double well system without detailed balance, in the weak noise limit. The pattern may contain cusps and other singular features, which are similar to the caustics of geometrical optics. Their presence is reflected in the quasipotential of the system, much as phase transitions are reflected in the free energy of a thermodynamic system. By tuning system parameters, a cusp may be made to coincide with the saddle point. Such an anomalous cusp is analogous to a nonclassical critical point. We derive a scaling law, and nonpolynomial `equations of state', that govern its bifurcation into conventional cusps.