Escape over barriers in almost integrable systems

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Abstract
Whenever the escaping entity and the thermal reservoir in contact with it move at comparable rates, escape must be viewed as due to diffusion in the space of the action variables. For almost integrable systems, the effective barrier height is argued to exceed substantially the potential-energy barrier of conventional theory, at least in the common case in which the potential barrier arises from terms in the Hamiltonian responsible for the nonintegrability, and to the extent that the usual quasiperturbative treatment of almost integrable systems is applicable at energies of order of the barrier.