82 citations · 362 across the 21 of their papers we have counts for
22 papers
Continuum Fibonacci Schrödinger Operators in the Strongly Coupled Regime
David Damanik, Mark Embree, Jake Fillman +2
We study Schrödinger operators on the real line whose potentials are generated by the Fibonacci substitution sequence and a rule that replaces symbols by compactly supported potent…
Localization for Random Schrödinger Operators Defined by Block Factors
David Damanik, Anton Gorodetski, Victor Kleptsyn
We consider discrete one-dimensional Schrödinger operators with random potentials obtained via a block code applied to an i.i.d. sequence of random variables. It is shown that, alm…
The Spectrum of Schrödinger Operators with Randomly Perturbed Ergodic Potentials
Artur Avila, David Damanik, Anton Gorodetski
We consider Schrödinger operators in whose potentials are given by the sum of an ergodic term and a random term of Anderson type. Under the assumption that the…
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…
Multidimensional Almost-Periodic Schrödinger Operators with Cantor Spectrum
David Damanik, Jake Fillman, Anton Gorodetski
We construct multidimensional almost-periodic Schrödinger operators whose spectrum has zero lower box counting dimension. In particular, the spectrum in these cases is a generalize…
Sums of regular Cantor sets of large dimension and the Square Fibonacci Hamiltonian
David Damanik, Anton Gorodetski
We show that under natural technical conditions, the sum of a dynamically defined Cantor set with a compact set in most cases (for almost all parameters) has positive Lebesgu…