Consider the Anderson model given by the Hamiltonian $H \in B(l^2( \mathbb{Z}^d)) $ defined by $H = - \Delta + V$ where the potential $V$ acts on a unit vector $ \mid {x} \rangle  \in l^2( \mathbb{Z}^d)$ by $V \mid {x} \rangle = V(x) \mid {x} \rangle $ where $V(x)$ are i.i.d uniformly distributed in $\lbrack 0,1 \rbrack$. This system exhibits Anderson localization.

Now, if we put $d=1$ and I pick $V(2x) $ i.i.d uniformly distributed in $\lbrack 0,1 \rbrack$ and then let $V(2x+1) = V(2x)$. Does this system then still exhibit Anderson localization?


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