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This is a Quantitative Study study.

October 19, 2025Open Access

Semi-classical limit of quantum scattering states for the nonlinear Hartree equation

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This analysis shows small-data scattering for quantum particles in the Hartree equation, indicating parallels with classical dynamics.

Small-data solutions scatter while obeying dispersion bounds, independent of the reduced Planck constant.
Wigner transforms of quantum scattering states converge weakly-* to classical scattering states for the Vlasov equation.
A new uniform dispersion estimate is crucial for analyzing singular interaction potentials like inverse power-law potentials.
Results highlight the dynamics of quantum systems and support classical behavior under weakly interacting conditions.

Hadama et al. (2025) studied this question.

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