2006/08/31 by Ram Band, Talia Shapira, Uzy Smilansky
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics #math-ph #math.MP #nlin.CD
paper · pdf · doi:10.1088/0305-4470/39/45/009
openalex publication_date 2006/10/24 · arxiv created 2006/12/17 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/31
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.