3 citations · 6 across the 6 of their papers we have counts for
6 papers
Multidimensional Schrödinger Operators Whose Spectrum Features a Half-Line and a Cantor Set
David Damanik, Jake Fillman, Anton Gorodetski
We construct multidimensional Schrödinger operators with a spectrum that has no gaps at high energies and that is nowhere dense at low energies. This gives the first example for wh…
Positive Lyapunov Exponents and a Large Deviation Theorem for Continuum Anderson Models, Briefly
Valmir Bucaj, David Damanik, Jake Fillman +4
In this short note, we prove positivity of the Lyapunov exponent for 1D continuum Anderson models by leveraging some classical tools from inverse spectral theory. The argument is m…
Spectra of Discrete Two-Dimensional Periodic Schrödinger Operators with Small Potentials
Mark Embree, Jake Fillman
We show that the spectrum of a discrete two-dimensional periodic Schrödinger operator on a square lattice with a sufficiently small potential is an interval, provided the period is…
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…
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…
Spectral Homogeneity of Discrete One-Dimensional Limit-Periodic Operators
Jake Fillman
We prove that a dense subset of limit periodic operators have spectra which are homogeneous Cantor sets in the sense of Carleson. Moreover, by using work of Egorova, our examples h…