30 citations · 116 across the 11 of their papers we have counts for
9 papers · 1 filter
Spectral Determinants of Almost Equilateral Quantum Graphs
Jonathan Harrison, Tracy Weyand
Kirchoff's matrix tree theorem of 1847 connects the number of spanning trees of a graph to the spectral determinant of the discrete Laplacian [22]. Recently an analogue was obtaine…
Quantizing graphs, one way or two?
Jon Harrison
Quantum graphs were introduced to model free electrons in organic molecules using a self-adjoint Hamiltonian on a network of intervals. A second graph quantization describes wave p…
Spectral Properties of Quantum Circulant Graphs
JM Harrison, E Swindle
We introduce a new model for investigating spectral properties of quantum graphs, a quantum circulant graph. Circulant graphs are the Cayley graphs of cyclic groups. Quantum circul…
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…
n-particle quantum statistics on graphs
Jonathan M. Harrison, Jonathan P. Keating, Jonathan M. Robbins +1
We develop a full characterization of abelian quantum statistics on graphs. We explain how the number of anyon phases is related to connectivity. For 2-connected graphs the indepen…
Finite pseudo orbit expansions for spectral quantities of quantum graphs
Ram Band, Jonathan M. Harrison, Christopher H. Joyner
We investigate spectral quantities of quantum graphs by expanding them as sums over pseudo orbits, sets of periodic orbits. Only a finite collection of pseudo orbits which are irre…