Escape dynamics of coupled particles in nonlinear, disordered lattices

Abstract

We consider the deterministic escape dynamics of a lattice chain of harmonically coupled particles from a metastable state over a one-dimensional potential barrier. While the case of periodic lattices has already been elaborated, the aim of the present work is to explore the extension to nonperiodic, i.e., disordered, lattices. Each particle evolves in an individual local potential, which is characterized by a harmonic term and a nonlinear term. Two kinds of parametric disorder are considered. "Disorder in nonlinearity" is only caused by different nonlinear terms--"disorder in harmonicity" only by different harmonic terms. We assure that the two kinds of disorder, with their individual potential barriers uniformly distributed around a globally equal mean barrier height, exhibit a comparable strength of disorder. Starting with an initial completely delocalized state, we observe localization of energy and formation of breathers ensues. It is shown that increasing disorder in nonlinearity decreases the mean escape time opposite to increasing mean escape times resulting from increased disorder in harmonicity. Comparison with the mean escape time obtained for a third kind of parametric disorder characterized by overall equal barrier heights leads to the conclusion that indeed inhomogeneous barriers facilitate the speedy escape.