The Sinai-Stadium billiard is a prototype example of chaotic geometries. Representative eigenfunctions of this geometry are shown here. The influence of the classical dynamical structures such as periodic orbits can be seen in some of the wavefunctions. The Sinai-Stadium was designed to have no non-isolated periodic orbits, which leads to deviation from universality.
Localization in Disordered Geometries
The basic geometry is a 44 x 21.8 cm rectangle with 1 cm square or circular tiles located randomly inside the rectangle. The tiles act as impurity scatterers (indicated by dots), and hence the geometry simulates a 2-D electron system with impurities. Sample wavefunctions for two such geometries with different amounts of “impurities” are shown. In a disordered geometry there are three length scales, (a) the size of the geometry, L, (b) the mean free path, l, and (c) the wave length of the resonance frequency which is used to probe the system. The most striking observation in the disordered geometries is the observation of localization, as predicted by Anderson. This effect is more pronounced in the lower eigenfunctions which are shown above.
Wavefunctions of a Disordered Geometry and a Chaotic Geometry
In these set of experiments, the effects of localization and chaos on the wavefunctions of chaotic and disordered geometries were addressed. As is expected the lower wavefunctions are more localized then the higher ones.