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math.DS2006
On non-perturbative Anderson localization for C^αpotentials generated by shifts and skew-shifts
Jackson Chan, Michael Goldstein, Wilhelm Schlag
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:…
math.DS2005
On resonances and the formation of gaps in the spectrum of quasi-periodic Schroedinger equations
Michael Goldstein, Wilhelm Schlag
We consider one-dimensional difference Schroedinger equations on the discrete line with a potential generated by evaluating a real-analytic potential function V(x) on the one-dimen…