24 citations · 163 across the 51 of their papers we have counts for
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math.SP2016
A condition for purely absolutely continuous spectrum for CMV operators using the density of states
Jake Fillman, Darren C. Ong
We prove an averaging formula for the derivative of the absolutely continuous part of the density of states measure for an ergodic family of CMV matrices. As a consequence, we show…
math.SP2016★ 2 cited
Purely Singular Continuous Spectrum for Limit-Periodic CMV Operators with Applications to Quantum Walks
Jake Fillman, Darren C. Ong
We show that a generic element of a space of limit-periodic CMV operators has zero-measure Cantor spectrum. We also prove a Craig--Simon type theorem for the density of states meas…
math.SP2016★ 24 cited
Ballistic Transport for Limit-Periodic Jacobi Matrices with Applications to Quantum Many-Body Problems
Jake Fillman
We study Jacobi matrices that are uniformly approximated by periodic operators. We show that if the rate of approximation is sufficiently rapid, then the associated quantum dynamic…