Propagation of arbitrary-order quantum velocity moments for Hartree dynamics

Establish propagation, uniformly in $\hbar$, of quantum velocity moments of arbitrary order for solutions of the Hartree equation.

Background

The discussion places the semiclassical Hartree-to-Vlasov problem in the context of uniform estimates in the semiclassical parameter. Beyond pointwise bounds on the wave function, controlling velocity moments of arbitrary order is identified as a related unresolved issue.

The paper explicitly reports that the cited work classifies this propagation problem as open. It is included as a distinct problem because it concerns a specific family of uniform-in-ℏ\hbar estimates rather than the broader Maxwell–Schrödinger-to-Vlasov–Maxwell limit.

References

The related problem of propagation of quantum velocity moments of arbitrary order uniformly in $\hbar$ for Hartree is explicitly classified as an open problem in .

— From the Maxwell-Schrödinger equation to the Euler-Maxwell equation in the semiclassical limit  (2610.11199 - Porat, 8 Oct 2026) in Section 1, “Background”