10 citations · 18 across the 7 of their papers we have counts for
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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…
Spectral Characteristics of Schrödinger Operators Generated by Product Systems
David Damanik, Jake Fillman, Philipp Gohlke
We study ergodic Schrödinger operators defined over product dynamical systems in which one factor is periodic and the other factor is either a subshift over a finite alphabet or an…
Gap Labelling for Discrete One-Dimensional Ergodic Schrödinger Operators
David Damanik, Jake Fillman
In this survey, we give an introduction to and proof of the gap labelling theorem for discrete one-dimensional ergodic Schrödinger operators via the Schwartzman homomorphism. To ke…
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…