45 citations · 163 across the 7 of their papers we have counts for
8 papers · 1 filter
Universality of nodal count distribution in large metric graphs
Lior Alon, Ram Band, Gregory Berkolaiko
An eigenfunction of the Laplacian on a metric (quantum) graph has an excess number of zeros due to the graph's non-trivial topology. This number, called the nodal surplus, is an in…
Quotients of graph operators by symmetry representations
Ram Band, Gregory Berkolaiko, Christopher H. Joyner +1
A finite dimensional operator that commutes with some symmetry group admits quotient operators, which are determined by the choice of associated representation. Taking the quotient…
Nodal Statistics On Quantum Graphs
Lior Alon, Ram Band, Gregory Berkolaiko
It has been suggested that the distribution of the suitably normalized number of zeros of Laplacian eigenfunctions contains information about the geometry of the underlying domain.…
Anomalous nodal count and singularities in the dispersion relation of honeycomb graphs
Ram Band, Gregory Berkolaiko, Tracy Weyand
We study the nodal count of the so-called bi-dendral graphs and show that it exhibits an anomaly: the nodal surplus is never equal to 0 or , the first Betti number of the graph.…
Universality of the momentum band density of periodic networks
Ram Band, Gregory Berkolaiko
The momentum spectrum of a periodic network (quantum graph) has a band-gap structure. We investigate the relative density of the bands or, equivalently, the probability that a rand…
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…
On the connection between the number of nodal domains on quantum graphs and the stability of graph partitions
Ram Band, Gregory Berkolaiko, Hillel Raz +1
Courant theorem provides an upper bound for the number of nodal domains of eigenfunctions of a wide class of Laplacian-type operators. In particular, it holds for generic eigenfunc…
Dynamics of nodal points and the nodal count on a family of quantum graphs
Ram Band, Gregory Berkolaiko, Uzy Smilansky
We investigate the properties of the zeros of the eigenfunctions on quantum graphs (metric graphs with a Schrödinger-type differential operator). Using tools such as scattering app…