Rui Han

Full measure reducibility and localization for quasiperiodic Jacobi operators: A topological criterion

Abstract We establish a topological criterion for connection between reducibility to constant rotations and dual localization, for the general family of analytic quasiperiodic Jacobi operators. As a corollary, we obtain the sharp arithmetic phase transition for the extended Harpers model in the positive Lyapunov exponent region.

Absence of Point Spectrum for the Self-Dual Extended Harper’S Model

We give a simple proof of absence of point spectrum for the self-dual extended Harpers model. We get a sharp result which improves that of Avila-Jitomirskaya-Marx in the isotropic self-dual regime.

Discrete Bethe-Sommerfeld Conjecture

In this paper, we prove a discrete version of the Bethe–Sommerfeld conjecture. Namely, we show that the spectra of multi-dimensional discrete periodic Schrödinger operators on

Uniform localization is always uniform

{\mathbb{Z}^d}

Quantum dynamical bounds for ergodic potentials with underlying dynamics of zero topological entropy

Zd lattice with sufficiently small potentials contain at most two intervals. Moreover, the spectrum is a single interval, provided at least one of the periods is odd, and can have a gap whenever all periods are even.