Ratchet universality in the bidirectional escape from a symmetric potential well

The present work discusses symmetry-breaking-induced bidirectional escape from a symmetric metastable potential well by the application of zero-average periodic forces in the presence of dissipation. We characterized the interplay between heteroclinic instabilities leading to chaotic escape and breaking of a generalized parity symmetry leading to directed ratchet escape to an attractor either at infinity or at -infinity. Optimal enhancement of directed ratchet escape is found to occur when the wave form of the zero-average periodic force acting on the damped driven oscillator matches as closely as possible to a universal wave form, as predicted by the theory of ratchet universality. Specifically, the optimal approximation to the universal force triggers the almost complete destruction of the nonescaping basin for driving amplitudes which are systematically lower than those corresponding to a symmetric periodic force having the same period. We expect that this work could be potentially useful in the control of elementary dynamic processes characterized by multidirectional escape from a potential well, such as forced chaotic scattering and laser-induced dissociation of molecular systems, among others.

Automated summary

This work discusses bidirectional escape from a symmetric metastable potential well induced by symmetry-breaking and how the optimal enhancement of directed ratchet escape is found to occur when the wave form of the zero-average periodic force matches a universal wave form. It also explores the destruction of the nonescaping basin for driving amplitudes systematically lower than those corresponding to a symmetric periodic force having the same period.