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We prove that the spectrum of the discrete Schr\"odinger operator on$\ell^2(Z^2)$, $(\psi_{n,m})\mapsto -(\psi_{n+1,m} +\psi_{n-1,m} +\psi_{n,m+1}+\psi_{n,m-1})+V_n\psi_{n,m}$ is absolutely continuous.

Absolute continuity of the spectrum of coupled identical systems on 1D lattices