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Nodal domains on isospectral quantum graphs: the resolution of isospectrality

Band, Ram, Shapira, Talia and Smilansky, Uzy 2006. Nodal domains on isospectral quantum graphs: the resolution of isospectrality. Journal of physics A Mathematical and general 39 (45) , pp. 13999-14014. 10.1088/0305-4470/39/45/009

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We present and discuss isospectral quantum graphs which are not isometric. These graphs are the analogues of the isospectral domains in which were introduced recently in Gordon et al (1992 Bull. Am. Math. Soc. 27 134–8), Chapman (1995 Am. Math. Mon. 102 124), Buser et al (1994 Int. Math. Res. Not. 9 391–400), Okada and Shudo (2001 J. Phys. A: Math. Gen. 34 5911–22), Jakobson et al (2006 J. Comput. Appl. Math. 194 141–55) and Levitin et al (2006 J. Phys. A: Math. Gen. 39 2073–82)) all based on Sunada's construction of isospectral domains (Sunada T 1985 Ann. Math. 121 196–86). After presenting some of the properties of these graphs, we discuss a few examples which support the conjecture that by counting the nodal domains of the corresponding eigenfunctions one can resolve the isospectral ambiguity.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Publisher: Institute of Physics and IOP Publishing
ISSN: 13616447
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Last Modified: 19 Mar 2016 22:04

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