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ROLE OF ENERGY EXCHANGE IN THE DETERMINISTIC ESCAPE OF A COUPLED NONLINEAR OSCILLATOR CHAIN

We consider the deterministic escape of a chain of harmonically coupled units from a metastable state over a cubic potential barrier. The underlying dynamics is conservative and noise-free. The supply of a sufficient total energy transforms the chain into the nonlinear regime from which an initially, nearly uniform lattice configuration becomes unstable, yielding a redistribution of energy. In an early stage of the dynamics, we estimate the degree of energy exchange enabling the coupled system to form strongly localized modes which eventually grow into a critical nucleus. Upon passing this transition state, the nonlinear chain performs a collective, deterministic escape. We analyze the associated nonlinear dynamics in phase space and relate the escape to diffusion in a separatrix layer.