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We prove maximal speed estimates for nonlinear quantum propagation in thecontext of the Hartree equation. More precisely, under some regularity andintegrability assumptions on the pair (convolution) potential, we construct aset of energy and space localized initial conditions such that, up totime-decaying tails, solutions starting in this set stay within the light coneof the corresponding initial datum. We quantify precisely the light cone speed,and hence the speed of nonlinear propagation, in terms of the momentum of theinitial state.

Maximal Speed of Quantum Propagation for the Hartree equation