arXiv subjects

Jackson Chan

Publications and source records attributed to Jackson Chan.

2 recordsLinked to original sources

arXiv2006

On non-perturbative Anderson localization for C^αpotentials generated by shifts and skew-shifts

In this paper we address the question of proving Anderson localization (AL) for the operator [H(x,ω)ψ](n) := - \vp(n+1) - \vp(n-1) + V\bigl(T^n_ωx\bigr)ψ(n), n\in\mathbb Z where T:\tor^2\to\tor^2 is either the shift or the skew-shift and V is only C^α(\tor^2) for some α>0. We show that under the assumption of positive Lyapunov exponents, (AL) takes place for a.e. frequency, phase, and energy.

math.DS↗

arXiv2005

Method of variations of potential of quasi-periodic Schrodinger equation

We study the one-dimensional discrete quasi-periodic Schrodinger equation. We introduce the notion of variations of potential and use it to define "typical" potential. We show that for typical C^3 potential, if the coupling constant is large, then for most frequencies, the Lyapunov exponent is positive for all energies.

math-ph↗