Counting nodal domains on surfaces of revolution

Karageorge, Panos D. and Smilansky, Uzy 2008. Counting nodal domains on surfaces of revolution. Journal of Physics A: Mathematical and Theoretical 41 (20) , 205102. 10.1088/1751-8113/41/20/205102

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Abstract

We consider eigenfunctions of the Laplace–Beltrami operator on special surfaces of revolution. For this separable system, the nodal domains of the (real) eigenfunctions form a checkerboard pattern, and their number νn is proportional to the product of the angular and the 'surface' quantum numbers. Arranging the wavefunctions by increasing values of the Laplace–Beltrami spectrum, we obtain the nodal sequence, whose statistical properties we study. In particular, we investigate the distribution of the normalized counts for sequences of eigenfunctions with K ≤ n ≤ K + ΔK, where . We show that the distribution approaches a limit as K, ΔK → ∞ (the classical limit), and study the leading corrections in the semi-classical limit. With this information, we derive the central result of this work: the nodal sequence of a mirror-symmetric surface is sufficient to uniquely determine its shape (modulo scaling).

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	IOP Publishing
ISSN:	1751-8121
Last Modified:	19 Mar 2016 22:24
URI:	https://orca.cardiff.ac.uk/id/eprint/15157

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