Abstract
We consider the scattering theory for discrete Schrödinger operators on \documentclass[12pt]{minimal}\begin{document}$\mathbb {Z}^d$\end{document}Zd with long-range potentials. We prove the existence of modified wave operators constructed in terms of solutions of a Hamilton-Jacobi equation on the torus \documentclass[12pt]{minimal}\begin{document}$\mathbb {T}^d$\end{document}Td.
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