10 citations · 30 across the 16 of their papers we have counts for
23 papers
Optimal dispersion for discrete periodic Schrödinger operators
David Damanik, Jake Fillman, Giorgio Young
We prove a dispersive estimate for periodic discrete Schrödinger operators on the line with optimal rate of decay. Additionally, by standard methods, we deduce dispersive estimates…
Comb domains of Schrödinger operators with small quasiperiodic potentials
Ilia Binder, David Damanik, Michael Goldstein +1
We characterize spectra of Schrödinger operators with small quasiperiodic analytic potentials in terms of their comb domains, and study action variables motivated by the KdV integr…
The Schwartzman Group of an Affine Transformation
David Damanik, Íris Emilsdóttir, Jake Fillman
We compute the Schwartzman group associated with an ergodic affine automorphism of a compact connected abelian group given by the composition of an automorphism of the group and a…
Gap Labels for Zeros of the Partition Function of the 1D Ising Model via the Schwartzman Homomorphism
David Damanik, Mark Embree, Jake Fillman
Inspired by the 1995 paper of Baake--Grimm--Pisani, we aim to explain the empirical observation that the distribution of Lee--Yang zeros corresponding to a one-dimensional Ising mo…
Discontinuities of the Integrated Density of States for Laplacians Associated with Penrose and Ammann-Beenker Tilings
David Damanik, Mark Embree, Jake Fillman +1
Aperiodic substitution tilings provide popular models for quasicrystals, materials exhibiting aperiodic order. We study the graph Laplacian associated with four tilings from the mu…
Johnson-Schwartzman Gap Labelling for Ergodic Jacobi Matrices
David Damanik, Jake Fillman, Zhenghe Zhang
We consider two-sided Jacobi matrices whose coefficients are obtained by continuous sampling along the orbits of a homeomorphim of a compact metric space. Given an ergodic probabil…