9 citations · 23 across the 5 of their papers we have counts for
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Zeta Functions of the Dirac Operator on Quantum Graphs
J. M. Harrison, T. Weyand, K. Kirsten
We construct spectral zeta functions for the Dirac operator on metric graphs. We start with the case of a rose graph, a graph with a single vertex where every edge is a loop. The t…
Vacuum energy of Schrödinger operators on metric graphs
J. M. Harrison, K. Kirsten
We present an integral formulation of the vacuum energy of Schrödinger operators on finite metric graphs. Local vertex matching conditions on the graph are classified according to…
Spectral determinants and zeta functions of Schrödinger operators on metric graphs
J. M. Harrison, K. Kirsten, C. Texier
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 clas…
Vacuum energy, spectral determinant and heat kernel asymptotics of graph Laplacians with general vertex matching conditions
J. M. Harrison, K. Kirsten
We consider Laplace operators on metric graphs, networks of one-dimensional line segments (bonds), with matching conditions at the vertices that make the operator self-adjoint. Suc…