On dynamical tunneling and classical resonances

Abstract

This letter establishes a firm relationship between classical nonlinear resonances and the phenomenon of dynamical tunneling. It is shown that the classical phase space with its hierarchy of resonance islands completely characterizes dynamical tunneling. In particular, it is not important to invoke criteria such as the size of the islands and presence or absence of avoided crossings for a consistent description of dynamical tunneling in near-integrable systems.