10 citations · 13 across the 4 of their papers we have counts for
7 papers
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…
Ergodic Schrödinger Operators in the Infinite Measure Setting
Michael Boshernitzan, David Damanik, Jake Fillman +1
We develop the basic theory of ergodic Schrödinger operators, which is well known for ergodic probability measures, in the case of a base dynamics on an infinite measure space. Thi…
Random Hamiltonians with Arbitrary Point Interactions
David Damanik, Jake Fillman, Mark Helman +2
We consider disordered Hamiltonians given by the Laplace operator subject to arbitrary random self-adjoint singular perturbations supported on random discrete subsets of the real l…
Zero Measure and Singular Continuous Spectra for Quantum Graphs
David Damanik, Licheng Fang, Selim Sukhtaiev
We introduce a dynamically defined class of unbounded, connected, equilateral metric graphs on which the Kirchhoff Laplacian has zero Lebesgue measure spectrum and a nontrivial sin…
Localization for Anderson Models on Metric and Discrete Tree Graphs
David Damanik, Jake Fillman, Selim Sukhtaiev
We establish spectral and dynamical localization for several Anderson models on metric and discrete radial trees. The localization results are obtained on compact intervals contain…