5 citations · 5 across the 3 of their papers we have counts for
4 papers
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…
Uniform positivity of the Lyapunov exponent for monotone potentials generated by the doubling map
Zhenghe Zhang
We show that for any doubling map generated monotone potential with derivative uniformly bounded away from zero, the Lyapunov exponent of the associated Schrödinger operators…
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…