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Intermediate wave-function statistics

Berkolaiko, G. (2003) Intermediate wave-function statistics. Physical Review Letters, 94 (13). p. 134103. ISSN 0031-9007

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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.

Item type: Article
ID code: 2118
Keywords: eigenfunctions, statistics, star graphs, orbits, mathematics, wave-function, Mathematics, Statistics, Physics and Astronomy(all)
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: 21 May 2015 08:31
URI: http://strathprints.strath.ac.uk/id/eprint/2118

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