34 citations · 117 across the 29 of their papers we have counts for
31 papers
Bounds on eigenvalue ratios of quantum graphs
Evans M. Harrell, James B. Kennedy, Gabriel J. Ramos
We study ratios of eigenvalues of the Laplacian on compact metric graphs. Our goals are threefold: First, we prove a sharp Ashbaugh--Benguria-type bound for the ratio of the first…
On the Fundamental Eigenvalues gap of Sturm-Liouville Operators
Mohammed Ahrami, Zakaria El Allali, Evans M. Harrell
We use methods of direct optimization as in [9] to find the minimizers of the fundamental gap of Sturm-Liouville operators on an interval, under the constraint that the potential i…
Optimizing the Fundamental Eigenvalue Gap of Quantum Graphs
Mohammed Ahrami, Zakaria El Allali, Evans M Harrell +1
We study the problem of minimizing or maximizing the fundamental spectral gap of Schrödinger operators on metric graphs with either a convex potential or a ``single-well'' potentia…
On topological states and secular equations for quantum-graph eigenvalues
Evans M. Harrell, Anna V. Maltsev
Quantum graphs without interaction which contain equilateral cycles possess "topological" bound states which do not correspond to zeroes of one of the two variants of the secular e…
Gaps between consecutive eigenvalues for compact metric graphs
David Borthwick, Evans M. Harrell, Haozhe Yu
On a compact metric graph, we consider the spectrum of the Laplacian defined with a mix of standard and Dirichlet vertex conditions. A Cheeger-type lower bound on the gap $λ_2 - λ_…
The heat kernel on the diagonal for a compact metric graph
David Borthwick, Kenny Jones, Evans M. Harrell
We analyze the heat kernel associated to the Laplacian on a compact metric graph, with standard Kirchoff-Neumann vertex conditions. An explicit formula for the heat kernel as a sum…