24 citations · 163 across the 51 of their papers we have counts for
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Gap Labels and Asymptotic Gap Opening for Full Shifts
David Damanik, Íris Emilsdóttir, Jake Fillman
We discuss gap labelling for operators generated by the full shift over a compact subset of the real line. The set of Johnson--Schwartzman gap labels is the algebra generated by we…
Mobility edges in pseudo-unitary quasiperiodic quantum walks
Christopher Cedzich, Jake Fillman
We introduce a Floquet quasicrystal that simulates the motion of Bloch electrons in a homogeneous magnetic field in discrete time steps. We admit the hopping to be non-reciprocal w…
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…
Absence of Bound States for Quantum Walks and CMV Matrices via Reflections
Christopher Cedzich, Jake Fillman
We give a criterion based on reflection symmetries in the spirit of Jitomirskaya--Simon to show absence of point spectrum for (split-step) quantum walks and Cantero--Moral--Velázqu…