Generic continuous spectrum for multi-dimensional quasi periodic Schrödinger operators with rough potentials

Rui Han, Fan Yang

We study the multi-dimensional operator $(H_{x}u{)}_n={\sum }_{|m-n|=1}{u}_m+f(T^n(x))u_n$, where $T$ is the shift of the torus $\T^d$. When $d=2$, we show the spectrum of $H_x$ is almos…