Phase space scars and quantum billiards

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5 Scopus citations


A semiclassical expression is derived for the spectral Wigner function of ergodic billiards in terms of a sum over contributions from classical periodic orbits. It represents a generalization of a similar formula by Berry, which does not immediately apply to billiard systems. These results are a natural generalization of Gutzwiller's trace formula for the density of states. Our theory clarifies the origin of scars in the eigenfunctions of billiard systems. However, in its present form, it is unable to predict what states will be dominated by individual periodic orbits. Finally, we compare some of the predictions of our theory with numerical results from the stadium. Within the limitations of numerical resolution, we find agreement between the two.

Original languageEnglish
Pages (from-to)121-140
Number of pages20
JournalZeitschrift für Physik B Condensed Matter
Issue number1
StatePublished - 1 Mar 1994


  • 03.65.Sq

ASJC Scopus subject areas

  • Condensed Matter Physics


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