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math.SP2026
Continuum Fibonacci Schrödinger Operators in the Strongly Coupled Regime
David Damanik, Mark Embree, Jake Fillman +2
We study Schrödinger operators on the real line whose potentials are generated by the Fibonacci substitution sequence and a rule that replaces symbols by compactly supported potent…
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★ 2 cited
Spectral Properties of Continuum Fibonacci Schrödinger Operators
Jake Fillman, May Mei
We study continuum Schrödinger operators on the real line whose potentials are comprised of two compactly supported square-integrable functions concatenated according to an element…