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math.SP2022
Discontinuities of the Integrated Density of States for Laplacians Associated with Penrose and Ammann-Beenker Tilings
David Damanik, Mark Embree, Jake Fillman +1
Aperiodic substitution tilings provide popular models for quasicrystals, materials exhibiting aperiodic order. We study the graph Laplacian associated with four tilings from the mu…
math.SP2017★ 3 cited
Spectra of Discrete Two-Dimensional Periodic Schrödinger Operators with Small Potentials
Mark Embree, Jake Fillman
We show that the spectrum of a discrete two-dimensional periodic Schrödinger operator on a square lattice with a sufficiently small potential is an interval, provided the period is…