Spectral determinants and zeta functions of Schrödinger operators on metric graphs

J. M. Harrison 1, K. Kirsten 1, C. Texier 2, 3

Journal of Physics A: Mathematical and Theoretical 45 (2012) 125206

A derivation of the spectral determinant of the Schrödinger operator on a metric graph is presented where the local matching conditions at the vertices are of the general form classified according to the scheme of Kostrykin and Schrader. To formulate the spectral determinant we first derive the spectral zeta function of the Schrödinger operator using an appropriate secular equation. The result obtained for the spectral determinant is along the lines of the recent conjecture.

  • 1. Department of Mathematics,
    Baylor University
  • 2. Laboratoire de Physique des Solides (LPS),
    CNRS : UMR8502 – Université Paris XI - Paris Sud
  • 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
    CNRS : UMR8626 – Université Paris XI - Paris Sud