We calculate statistical properties of the eigenfunctions of two quantum systems that exhibit intermediate spectral statistics: star graphs and Seba billiards. First, we show that these eigenfunctions are not quantum ergodic, and calculate the corresponding limit distribution. Second, we find that they can be strongly scarred, in the case of star graphs by short (unstable) periodic orbits and, in the case of Seba billiards, by certain families of orbits. We construct sequences of states which have such a limit. Our results are illustrated by numerical computations.
|Translated title of the contribution||Intermediate wave function statistics|
|Article number||art. no. 134103|
|Journal||Physical Review Letters|
|Publication status||Published - 26 Sep 2003|
Bibliographical notePublisher: American Physical Soc
Other identifier: IDS number 725ZX