On the Spectrum of the Surface Maryland Model

We study spectral properties of the discrete Laplacian H on the half space Z₊^d+1 = Z^d× Z₊ with a boundary condition (n,-1) = tan( ... n + )(n,0), where [0,1]^d. We denote by H₀ the Dirichlet Laplacian on Z₊^d+1. Whenever is independent over rationals (H) = R. Khoruzenko and Pastur have shown for a set of 's of Lebesgue measure 1, the spectrum of H on R (H₀) is pure point and that corresponding eigenfunctions decay exponentially. In this Letter we show that if is independent over rationals, then the spectrum of H on the set (H₀) is purely absolutely continuous.