Unusual quantum effects in scattering wavefunctions of two-dimensional cage potentials

Abstract

We exhibit long-lived resonances in scattering from two-dimensional soft cage potentials comprised of three and four Gaussian peaks. Specific low-energy resonances with very narrow width are shown to correspond to classical multiple-reflection events. These states have much larger probability densities inside the cage than outside and mimic bound states in the sense that the symmetry-breaking effect of the incident wave is relatively small. As a result, we have found that isolated states display the simple symmetry characteristics of bound states. Overlapping resonances exhibit a mixing of symmetry classes leading to wavefunctions of lower symmetry, like those of wider resonances at higher energy. We demonstrate that at energies below the lowest resonances of two-dimensional cages, where the distance across the entrance of the cage corresponds to less than half a wavelength, the wavefunction may still gain access to the interior region by squeezing its wavelength in the necessary direction at the expense of the kinetic energy in the direction normal to the opening. The resulting curvature of the wavefunction in the donor dimension corresponds to an imaginary wave number, curving away from the plane defined by zero amplitude. This mechanism for passing between obstacles may be relevant for electronic and optical devices having spatial structures with dimensions comparable to the wavelengths of the energy carriers.