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

Abstract

We prove that the spectrum of the discrete Schrödinger 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.