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

2008

Abstract : We consider a metric graph GG made of two graphs G1G1 and G2G2 attached at one point. We derive a formula relating the spectral determinant of the Laplace operator SG(γ)=det(γ−Δ)SG(γ)=det(γ−Δ) in terms of the spectral determinants of the two subgraphs. The result is generalized to describe the attachment of nn graphs. The formulae are also valid for the spectral determinant of the Schrödinger operator det(γ−Δ+V(x))det(γ−Δ+V(x)).

Auteur

Christophe Texier 1, 2
1 LPTMS – Laboratoire de Physique Théorique et Modèles Statistiques
2 LPS – Laboratoire de Physique des Solides