Phys. Rev. Lett. 91, 134103 (2003) [4 pages]Intermediate Wave Function StatisticsReceived 9 April 2003; published 26 September 2003 We calculate statistical properties of the eigenfunctions of two quantum systems that exhibit intermediate spectral statistics: star graphs and Šeba 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 Šeba billiards, by certain families of orbits. We construct sequences of states which have such a limit. Our results are illustrated by numerical computations. © 2003 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.91.134103
DOI:
10.1103/PhysRevLett.91.134103
PACS:
05.45.Mt
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