The spectra of surface Maryland model for all phases
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abstract
We study the discrete Schr"{o}dinger operators $H_{lambda,alpha, heta}$ on $ell^2(mathbb{Z}^{d+1})$ with surface potential of the form $V(n,x)=lambda delta(x) anpi(alphacdot n+ heta)$, and $H_{lambda,alpha, heta}^{+}$ on $ell^2(mathbb{Z}^{d} imes mathbb{Z}_+)$ with the boundary condition $ psi_{(n,-1)}=lambda anpi(alphacdot n+ heta)psi_{(n,0)} $, where $alphain mathbb{R}^d$ is rationally independent. We show that the spectra of $H_{lambda,alpha, heta}$ and $H_{lambda,alpha, heta}^{+}$ are $(-infty,infty)$ for all parameters. We can also determine the absolutely continuous spectra and Hausdorff dimension of the spectral measures if $d=1$.
