The exterior and interior edge states of magnetic billiards: Spectral statistics and correlations

We study the properties of quantum states in the interior and the exterior of magnetic billiards. A weight is associated to each state, providing an objective criterion to distinguish between bulk and edge states. We define a spectral density of edge states, which is then studied statistically and semiclassically. In particular, we observe strong cross-correlations between the interior and exterior edge spectra. They are identified as the quantum signature of a classical duality of periodic orbits.