We study the "finger-prints" of classical chaos in quantum mechanics. The subjects which interested us most during the past few years were:

Correlations between periodic orbit and in the spectra of their actions

Magnetic edge-states and the duality of the interior and the exterior energy spectra

Correlated periodic orbits for the 3-D Sinai billiard

Interior and exterior wave functions for a magnetic ellipse billiard.  The wave-functions concentrate along dual classical trajectories in the interior (red) and exterior (blue)

Quantum Graphs

The nodal set of chatoic wave-functions, counting nodal domains, random waves

The nearest-neighbor statistics for the spectrum of a connected 4-vertices graph (tetrahedron).  This numerical simulation was the starting point for our work on quantum graphs

The nodal structure of a typical high lying eigenfunction in a chaotic stadium (billiard)