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arXiv · 2202.13998

Global-in-time Semiclassical Regularity for the Hartree-Fock Equation

Jacky J. Chong·Laurent Lafleche·Chiara Saffirio
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Abstract

For arbitrarily large times $T>0$, we prove the uniform-in-$\hbar$ propagation of semiclassical regularity for the solutions to the Hartree$\unicode{x2013}$Fock equation with singular interactions of the form $V(x)=\pm\,|x|^{-a}$ where $a\in(0,\frac12)$. As a byproduct of this result, we extend to arbitrarily long times the derivation of the Hartree$\unicode{x2013}$Fock and the Vlasov equations from the many-body dynamics provided in [J. Chong, L. Lafleche, C. Saffirio: arXiv:2103.10946 (2021)].

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Jacky J. Chong, Laurent Lafleche, Chiara Saffirio. 2022-02-28. Global-in-time Semiclassical Regularity for the Hartree-Fock Equation. https://doi.org/10.1063/5.0089741

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