Maximal scarring for eigenfunctions of quantum star graphs

We prove the existence of scarred eigenstates for star graphs with Fourier transform scattering matrices at the central vertex.  The scarred states are half-delocalised on a single bond.  Moreover we prove that the scarred states we construct are maximal in the sense that it is impossible to have quantum eigenfunctions with a significantly lower entropy than our examples.

This talk is based on joint work with G. Berkolaiko.