Spectral determinant on graphs with generalized boundary conditions

Jean Desbois ¹

European Physical Journal B 24 (2001) 261-266

The spectral determinant of the Schrödinger operator ($ – \Delta + V(x) $) on a graph is computed for general boundary conditions. ($\Delta$ is the Laplacian and $V(x)$ is some potential defined on the graph). Applications to restricted random walks on graphs are discussed.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
  CNRS : UMR8626 – Université Paris XI – Paris Sud