27 citations · 120 across the 24 of their papers we have counts for
30 papers
Homogenized graphs with spectrally embedded defect states
Kirill D. Cherednichenko, Stephen P. Shipman
By homogenizing high-contrast periodic metric graphs, we create continuous media that admit bound states produced by local defects at energies embedded in the continuous spectrum.…
Algebraic Aspects of Periodic Graph Operators
Stephen P. Shipman, Frank Sottile
A periodic linear graph operator acts on states (functions) defined on the vertices of a graph equipped with a free translation action. Fourier transform with respect to the transl…
Stable defect states in the continuous spectrum of bilayer graphene with magnetic field
Stephen P. Shipman, Jorge Villalobos
In a tight-binding model of AA-stacked bilayer graphene, it is demonstrated that a bound defect state within the region of continuous spectrum can exist stably with respect to vari…
The inverse problem for a spectral asymmetry function of the Schrödinger operator on a finite interval
B. Malcolm Brown, Karl Michael Schmidt, Stephen P. Shipman +1
For the Schrödinger equation on a finite -interval, there is defined an "asymmetry function" , which is entire of order and type in…
Infinitely many embedded eigenvalues for the Neumann-Poincaré operator in 3D
Wei Li, Karl-Mikael Perfekt, Stephen P. Shipman
This article constructs a surface whose Neumann-Poincaré (NP) integral operator has infinitely many eigenvalues embedded in its essential spectrum. The surface is a sphere perturbe…
Spectra of Regular Quantum Trees: Rogue Eigenvalues and Dependence on Vertex Condition
Zhaoxia W. Hess, Stephen P. Shipman
We investigate the spectrum of Schrödinger operators on finite regular metric trees through a relation to orthogonal polynomials that provides a graphical perspective. As the Robin…