10 citations · 14 across the 9 of their papers we have counts for
17 papers
On Simon's Hausdorff Dimension Conjecture
David Damanik, Jake Fillman, Shuzheng Guo +1
Barry Simon conjectured in 2005 that the Szegő matrices, associated with Verblunsky coefficients obeying for…
Ballistic Transport for Periodic Jacobi Operators on
Jake Fillman
In this expository work, we collect some background results and give a short proof of the following theorem: periodic Jacobi matrices on exhibit strong ballistic mot…
Zero Measure Spectrum for Multi-Frequency Schrödinger Operators
Jon Chaika, David Damanik, Jake Fillman +1
Building on works of Berthé--Steiner--Thuswaldner and Fogg--Nous we show that on the two-dimensional torus, Lebesgue almost every translation admits a natural coding such that the…
Schrödinger Operators with Thin Spectra
David Damanik, Jake Fillman
The determination of the spectrum of a Schrödinger operator is a fundamental problem in mathematical quantum mechanics. We discuss a series of results showing that Schrödinger oper…
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…
Singular continuous Cantor spectrum for magnetic quantum walks
C. Cedzich, J. Fillman, T. Geib +1
In this note, we consider a physical system given by a two-dimensional quantum walk in an external magnetic field. In this setup, we show that both the topological structure as wel…