On the Nodal Count Statistics for Separable Systems in any Dimension
arXiv:1208.2120 · doi:10.1088/1751-8113/46/4/045201
Abstract
We consider the statistics of the number of nodal domains aka nodal counts for eigenfunctions of separable wave equations in arbitrary dimension. We give an explicit expression for the limiting distribution of normalised nodal counts and analyse some of its universal properties. Our results are illustrated by detailed discussion of simple examples and numerical nodal count distributions.
21 pages, 4 figures
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