9 papers · 1 filter
Computing Spectral Size: Rigorous Algorithms and the Limits of Computation
Matthew J. Colbrook, Mark Embree, Jake Fillman
Many structures in mathematical physics and dynamics exhibit intricate fractal geometry. Such behavior appears prominently in quantum mechanics and materials science through spectr…
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 poten…
Absence of ballistic motion and presence of almost-ballistic motion for unitary operators with pure point spectrum
Christopher Cedzich, Jake Fillman, Luis Velázquez
We adapt two results of Simon and collaborators to the setting of discrete-time unitary dynamics. We show that pure point spectrum precludes ballistic motion, and exhibit a family…
Thin Spectra for Periodic and Ergodic Word Models
Jake Fillman, Michala N. Gradner, Hannah J. Hendricks
We establish a new and simple criterion that suffices to generate many spectral gaps for periodic word models. This leads to new examples of ergodic Schrödinger operators with Can…
Measure of the spectra of periodic graph operators in the large-coupling limit
Jake Fillman
We derive a sharp criterion on the spectra of periodic discrete Schrödinger operators acting on connected periodic lattices: the measure of the spectrum goes to zero as the coupli…
Optimal dispersion for discrete periodic Schrödinger operators
David Damanik, Jake Fillman, Giorgio Young
We prove a dispersive estimate for periodic discrete Schrödinger operators on the line with optimal rate of decay. Additionally, by standard methods, we deduce dispersive estimate…