On the spectrum of the Laplace operator of metric graphs attached at a vertex -- Spectral determinant approach

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dc.creatorTexier, Christophe
dc.date2007-06-01
dc.date2008-02-19
dc.date.accessioned2026-07-07T09:21:19Z
dc.date.available2026-07-07T09:21:19Z
dc.descriptionWe consider a metric graph $\mathcal{G}$ made of two graphs $\mathcal{G}_1$ and $\mathcal{G}_2$ attached at one point. We derive a formula relating the spectral determinant of the Laplace operator $S_\mathcal{G}(γ)=\det(γ-Δ)$ in terms of the spectral determinants of the two subgraphs. The result is generalized to describe the attachment of $n$ graphs. The formulae are also valid for the spectral determinant of the Schrödinger operator $\det(γ-Δ+V(x))$.
dc.descriptionLaTeX, 8 pages, 7 eps figures, v2: new appendix, v3: discussions and ref added
dc.identifierhttps://arxiv.org/abs/0706.0120
dc.identifierhttp://arxiv.org/abs/0706.0120
dc.identifierJ. Phys. A: Math. Theor. 41 (2008) 085207
dc.identifierdoi:10.1088/1751-8113/41/8/085207
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/154981
dc.subjectMathematical Physics
dc.subjectMesoscale and Nanoscale Physics
dc.titleOn the spectrum of the Laplace operator of metric graphs attached at a vertex -- Spectral determinant approach
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