On the nodal count statistics for separable systems in any dimension

We consider the statistics of the number of nodal domains aka nodal counts for eigenfunctions of separable wave equations in an arbitrary dimension. We give an explicit expression for the limiting distribution of normalized nodal counts and analyse some of its universal properties. Our results are i...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2013-02, Vol.46 (4), p.45201-18
Main Authors: Gnutzmann, Sven, Lois, Stylianos
Format: Article
Language:English
Subjects:
Constraining
Counting
Eigenfunctions
Mathematical models
nodal sets and nodal domains
semiclassical methods
Statistics
Wave equations
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Summary:We consider the statistics of the number of nodal domains aka nodal counts for eigenfunctions of separable wave equations in an arbitrary dimension. We give an explicit expression for the limiting distribution of normalized nodal counts and analyse some of its universal properties. Our results are illustrated by the detailed discussion of simple examples and numerical nodal count distributions.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/46/4/045201