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.

9 pages with 3 figures, uses REVTeX and epsfig

References in corpus (5)

• Asymptotic Exit Location Distributions in the Stochastic Exit Problem
• A Scaling Theory of Bifurcations in the Symmetric Weak-Noise Escape Problem
• Observable and hidden singular features of large fluctuations in nonequilibrium systems
• The Effect of Focusing and Caustics on Exit Phenomena in Systems Lacking Detailed Balance
• Experiments on Critical Phenomena in a Noisy Exit Problem

Cited by in corpus (7)

• Structure of Stochastic Dynamics near Fixed Points
• Laws in Darwinian Evolutionary Theory
• Singularities in large deviation functions
• Large-deviation principles, stochastic effective actions, path entropies, and the structure and meaning of thermodynamic descriptions
• Cusp singularities in boundary-driven diffusive systems
• Critical Behavior of the Kramers Escape Rate in Asymmetric Classical Field Theories
• Investigation on the properties of Sine-Wiener noise and its induced escape in the particular limit case $D\to \infty$