Intermediate wave-function statistics

Berkolaiko, G. (2003) Intermediate wave-function statistics. Physical Review Letters, 94 (13). p. 134103. ISSN 1079-7114 (http://dx.doi.org/10.1103/PhysRevLett.91.134103)

Abstract

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.

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• Item metadata

  Item type:	Article
  ID code:	2118
  Dates:	Date Event 2003 Published
  Subjects:	Science > Mathematics Social Sciences > Statistics
  Department:	Faculty of Science > Mathematics and Statistics > Mathematics
  Depositing user:	Strathprints Administrator
  Date deposited:	17 Nov 2006
  Last modified:	08 Apr 2024 15:25
  URI:	https://strathprints.strath.ac.uk/id/eprint/2118