Time-dependent harmonic oscillator and spectral determinant on graphs
Laboratoire de Physique Théorique et Modèles Statistiques,
Université Paris-Sud, bâtiment 100, 91405 Orsay Cedex, France
Published online: 15 May 2000
Using a path integral approach and also considerations about the time-dependent harmonic oscillator, we compute the spectral determinant of the operator (-Δ+V(x)) on a graph. (Δ is the Laplacian and V(x) is some potential defined on the graph). We recover a recent result that was obtained by constructing the Green's function on the graph. We also extend those considerations to the case when i) a magnetic field is added to the system, ii) the potential, V(x), contains repulsive δ peaks.
PACS: 02.70.-c – Computational techniques / 03.65.-w – Quantum mechanics / 11.10.-z – Field theory
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000