Abstract
A perturbation theory is developed for the level splitting due to dynamical tunneling in two-dimensional billiards. Using a scattering-matrix approach, the splittings are expressed in terms of a matrix element connecting quasimodes localized in the subspace of positive and negative angular momentum, in analogy to the familiar degenerate double-well problem. The theory is shown to work well for billiards which are integrable, mixed, and strongly chaotic.
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