38 citations · 90 across the 9 of their papers we have counts for
9 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…
Cantor spectrum for a class of quasiperiodic Schrödinger operators
Yiqian Wang, Zhenghe Zhang
We show that for a class of quasiperiodic potentials and for any Diophantine frequency, the spectrum of the corresponding Schrödinger operators is Cantor. Our approach is of…
Uniform Positivity and Continuity of Lyapunov Exponents for a Class of Quasiperiodic Schrödinger Cocycles
Yiqian Wang, Zhenghe Zhang
We show that for a class of quasiperiodic potentials and for any Diophantine frequency, the Lyapunov exponents of the corresponding Schrödinger cocycles are uniformly positiv…
Uniform hyperbolicity and its relation with spectral analysis of 1D discrete Schrödinger Operators
Zhenghe Zhang
This paper intends to provide new, simple, and self-contained proofs of the equivalence of various different descriptions of the uniformly hyperbolic seq…
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…
Positive Lyapunov Exponents for Quasiperiodic Szego cocycles
Zhenghe Zhang
In this paper we first obtain a formula of averaged Lyapunov exponents for ergodic Szego cocycles via the Herman-Avila-Bochi formula. Then using acceleration, we construct a class…