33 citations · 33 across the 3 of their papers we have counts for
4 papers
Spectral statistics of preferred orientation quantum graphs
Ram Band, Pavel Exner, Divya Goel +1
We study the spectral statistics of quantum (metric) graphs whose vertices are equipped with preferred orientation vertex conditions. When comparing their spectral statistics to th…
Sturm-Hurwitz Theorem for quantum graphs
Ram Band, Philippe Charron
We prove upper and lower bounds for the number of zeroes of linear combinations of Schrödinger eigenfunctions on metric (quantum) graphs. These bounds are distinct from both the in…
Quantum graphs which optimize the spectral gap
Ram Band, Guillaume Lévy
A finite discrete graph is turned into a quantum (metric) graph once a finite length is assigned to each edge and the one-dimensional Laplacian is taken to be the operator. We stud…
The Nodal Count {0, 1, 2, 3,...} Implies The Graph is a Tree
Ram Band
Sturm's oscillation theorem states that the n-th eigenfunction of a Sturm-Liouville operator on the interval has n-1 zeros (nodes). This result was generalized for all metric tree…