For arbitrarily large times T>0, we prove the uniform-in-ℏ propagation of semiclassical regularity for the solutions to the Hartreex2013Fock equation with singular interactions of the form V(x)=±∣x∣−a
Nearby in the stack
where
a∈(0,21)
. As a byproduct of this result, we extend to arbitrarily long times the derivation of the Hartree
x2013
Fock and the Vlasov equations from the many-body dynamics provided in [J. Chong, L. Lafleche, C. Saffirio: arXiv:2103.10946 (2021)].