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math.SP2021★ 14 cited
Almost Everything About the Unitary Almost Mathieu Operator
Christopher Cedzich, Jake Fillman, Darren C. Ong
We introduce a unitary almost-Mathieu operator, which is obtained from a two-dimensional quantum walk in a uniform magnetic field. We exhibit a version of Aubry--André duality for…
math.SP2021
Thin Spectra and Singular Continuous Spectral Measures for Limit-Periodic Jacobi Matrices
David Damanik, Jake Fillman, Chunyi Wang
This paper investigates the spectral properties of Jacobi matrices with limit-periodic coefficients. We show that for a residual set of such matrices, the spectrum is a Cantor set…