Value distribution of the eigenfunctions and spectral determinants of quantum star graphs

JP Keating, J Marklof, B Winn

Research output: Contribution to journalArticle (Academic Journal)peer-review

22 Citations (Scopus)

Abstract

We compute the value distributions of the eigenfunctions and spectral determinant of the Schrodinger operator on families of star graphs. The values of the spectral determinant are shown to have a Cauchy distribution with respect both to averages over bond lengths in the limit as the wavenumber tends to infinity and to averages over wavenumber when the bond lengths are fixed and not rationally related. This is in contrast to the spectral determinants of random matrices, for which the logarithm is known to satisfy a Gaussian limit distribution. The value distribution of the eigenfunctions also differs from the corresponding random matrix result. We argue that the value distributions of the spectral determinant and of the eigenfunctions should coincide with those of Seba-type billiards.
Translated title of the contributionValue distribution of the eigenfunctions and spectral determinants of quantum star graphs
Original languageEnglish
Pages (from-to)421 - 452
Number of pages32
JournalCommunications in Mathematical Physics
Volume241 (2-3)
DOIs
Publication statusPublished - Oct 2003

Bibliographical note

Publisher: Springer-Verlag
Other identifier: IDS number 743TA

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