24 citations · 163 across the 51 of their papers we have counts for
3 papers · 1 filter
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…
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…
Irreducibility of the Bloch Variety for Finite-Range Schrödinger Operators
Jake Fillman, Wencai Liu, Rodrigo Matos
We study the Bloch variety of discrete Schrödinger operators associated with a complex periodic potential and a general finite-range interaction, showing that the Bloch variety is…