Evanescent coupling between discs: a model for near-integrable tunnelling

Abstract

An analysis is provided of the splitting due to tunnelling of the energy levels in two-dimensional double-disk potentials. The formal setting of this problem is similar to that of tunnelling between tori in the near-integrable regime but is free of the difficulties arising from the existence of natural boundaries that are generic to such problems, enabling a systematic investigation of the relevant semiclassical theory. The semiclassical predictions are found to be consistent with exponentially accurate results obtained following reduction to a boundary-value problem. A numerical quantization is also performed and found to agree with the approximate results.