When It Helps to Be Purely Hamiltonian: Acceleration of Rare Events and Enhanced Escape Dynamics

Abstract

We consider the self-organized escape of a linear chain of coupled units from a metastable state over a barrier in a microcanonical situation.Initially the units of the chain are situated near the bottom of the potential well forming a flat state. In the underlying conservative and deterministic dynamics such a uniform and linear lattice state with comparatively little energy content seems to be restrained to oscillations around the potential bottom preventing escape from the well. It is demonstrated that even small deviations from the flat state entail internal energy redistribution leading to such strong localization that the lattice chain spontaneously adopts a localized pattern resembling a hairpin-like structure. The latter corresponds to a critical equilibrium configuration, that is a transition state, and, being dynamically unstable, constitutes the starting point for the escape process. The collective barrier crossing of the units takes place as ∈dex{kink-antikink motion}kink-antikink motions along the chain. It turns out that this nonlinear barrier crossing in a microcanonical situation is more efficient compared with a thermally activated chain for small ratios between the total energy of the chain and the barrier energy.