Discrete Schrödinger operators on Z^d with V_n = o(|n|^{-1}) have purely absolutely continuous spectrum and exhibit ballistic transport where weighted position moments grow as t^r for AC initial states.
Differential Equations 29 (1978), 289–296
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Ballistic Transport for Discrete Multi-Dimensional Schr\"odinger Operators With Decaying Potential
Discrete Schrödinger operators on Z^d with V_n = o(|n|^{-1}) have purely absolutely continuous spectrum and exhibit ballistic transport where weighted position moments grow as t^r for AC initial states.