Counting open nodal lines of random waves on planar domains

Details Counting open nodal lines of random waves on planar domains Counting open nodal lines of random waves on planar domains

2008-10-07

arxiv.org/abs/0810.1276v4

Physics

Mathematical Physics

1) We simplified the proof of the converse direction in Lemma 2.1. 2) We moved the proof of Prop. 3.2 (and Lemma 3.1) to the a

Scientific paper

We compute the asymptotic expectation of the number of {\em open} nodal lines for random waves on smooth planar domains. We find that for both the long energy window $[0,\lambda]$ and the short one $[\lambda,\lambda+1]$ the expected number of open nodal lines is proportional to $\lambda$, asymptotically as $\lambda\to\infty$. Our results are consistent with the predictions in the physics literature made by Blum, Gnutzmann and Smilansky \cite{BGS}.

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