Intermediate Wave Function Statistics

G. Berkolaiko, J. P. Keating, and B. Winn
Phys. Rev. Lett. 91, 134103 – Published 26 September 2003

Abstract

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.

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  • Received 9 April 2003

DOI:https://doi.org/10.1103/PhysRevLett.91.134103

©2003 American Physical Society

Authors & Affiliations

G. Berkolaiko1, J. P. Keating2, and B. Winn2,*

  • 1Department of Mathematics, University of Strathclyde, Glasgow G1 1XH, United Kingdom
  • 2School of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom

  • *Electronic address: b.winn@bristol.ac.uk

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Vol. 91, Iss. 13 — 26 September 2003

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