Three disks in a row: A two-dimensional scattering analog of the double-well problem.

We investigate the scattering off three non-overlapping disks equidistantly spaced along a line in the two-dimensional plane with the radii of the outer disks equal and the radius of the inner disk varied. This system is a two-dimensional scattering analog to the double-well-potential (bound state) problem in one dimension. In both systems the symmetry-splittings between symmetric and anti-symmetric states or resonances, respectively, have to be traced back to tunneling effects, as semiclassically the geometrical periodic orbits have no contact with the vertical symmetry axis. We construct the leading semiclassical “creeping” orbits which are responsible for the symmetry-splitting of the resonances in this system. The collinear threedisk-system is not only one of the simplest but also one of the most effective systems for detecting creeping phenomena. While in symmetrically placed n-disk systems creeping corrections affect the sub-leading resonances, they here alone determine the symmetry splitting of the 3-disk resonances in the semiclassical calculation. It should therefore be considered as a paradigm for the study of both theoretical and experimental creeping effects. PACS numbers: 03.20.+i, 03.65.Sq, 05.45.+b