38 citations · 90 across the 9 of their papers we have counts for
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Schrödinger Operators with Potentials Generated by Hyperbolic Transformations: II. Large Deviations and Anderson Localization
Artur Avila, David Damanik, Zhenghe Zhang
We consider discrete one-dimensional Schrödinger operators whose potentials are generated by Hölder continuous sampling along the orbits of a uniformly hyperbolic transformation. F…
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…
Spectral Characteristics of the Unitary Critical Almost-Mathieu Operator
Jake Fillman, Darren C. Ong, Zhenghe Zhang
We discuss spectral characteristics of a one-dimensional quantum walk whose coins are distributed quasi-periodically. The unitary update rule of this quantum walk shares many spect…
Singular Density of States Measure for Subshift and Quasi-Periodic Schrödinger Operators
Artur Avila, David Damanik, Zhenghe Zhang
Simon's subshift conjecture states that for every aperiodic minimal subshift of Verblunsky coefficients, the common essential support of the associated measures has zero Lebesgue m…