83 citations · 288 across the 16 of their papers we have counts for
8 papers · 1 filter
Relating Zeta Functions of Discrete and Quantum Graphs
Jonathan Harrison, Tracy Weyand
We write the spectral zeta function of the Laplace operator on an equilateral metric graph in terms of the spectral zeta function of the normalized Laplace operator on the correspo…
Lyndon word decompositions and pseudo orbits on q-nary graphs
R. Band, J. M. Harrison, M. Sepanski
A foundational result in the theory of Lyndon words (words that are strictly earlier in lexicographic order than their cyclic permutations) is the Chen-Fox-Lyndon theorem which sta…
Intermediate statistics for a system with symplectic symmetry: the Dirac rose graph
J. M. Harrison, B. Winn
We study the spectral statistics of the Dirac operator on a rose-shaped graph---a graph with a single vertex and all bonds connected at both ends to the vertex. We formulate a secu…
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…
Zeta functions of quantum graphs
J. M. Harrison, K. Kirsten
In this article we construct zeta functions of quantum graphs using a contour integral technique based on the argument principle. We start by considering the special case of the st…