TRANSFER-MATRIX APPROACH TO TUNNELING BETWEEN KOLMOGOROV-ARNOLD-MOSERTORI

We consider splittings of the energies of degenerate quasimodes in a t wo-dimensional channel. This system is a model for splittings of degen eracies due to multidimensional tunneling in a general quasi-integrabl e system. We formulate a determinant quantization condition in terms o f the transfer matrix, which enables us to relate the splittings to el ements of the scattering matrix. We find that the splittings can be du e to either a single- or a multiple-scattering process. In the former case, the results reduce to an earlier theoretical analysis which used an assumption that the splittings are canonically invariant quantitie s. We demonstrate a quantitative agreement between semiclassical theor y and numerical calculations of the splittings.