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math.SP2026
On the identification of certain classes of gap-rich sets
Jake Fillman, Yi-Sheng Lim
The notion of gap-richness was recently introduced to quantify the ability to open spectral gaps for periodic word models by arbitrarily small perturbations and is useful in the co…
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.SP2026
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…