Enhanced Stability in Quantum Optimal Transport Pseudometrics: From Hartree to Vlasov-Poisson

Abstract

In this paper we establish almost-optimal stability estimates in quantum optimal transport pseudometrics for the semiclassical limit of the Hartree dynamics to the Vlasov-Poisson equation, in the regime where the solutions have bounded densities. We combine Golse and Paul's method from [Arch. Ration. Mech. Anal. 223:57-94, 2017], which uses a semiclassical version of the optimal transport distance and which was adapted to the case of the Coulomb and gravitational interactions by the second author in [J. Stat. Phys. 177:20-60, 2019], with a new approach developed by the first author in [Arch. Ration. Mech. Anal. 244:27-50, 2022] to quantitatively improve stability estimates in kinetic theory.

arXiv comment18 pages

References in corpus (14)

• On the Mean Field and Classical Limits of Quantum Mechanics
• The Schrödinger Equation in the Mean-Field and Semiclassical Regime
• From the Hartree dynamics to the Vlasov equation
• The classical limit of the time dependent Hartree-Fock equation. I. The Weyl symbol of the solution
• Quasineutral limit for Vlasov-Poisson via Wasserstein stability estimates in higher dimension
• Propagation of Moments and Semiclassical Limit from Hartree to Vlasov Equation
• Semiclassical limit to the Vlasov equation with inverse power law potentials
• Strong and weak semiclassical limits for some rough Hamiltonians
• Global Semiclassical Limit from Hartree to Vlasov Equation for Concentrated Initial Data
• A mean field approach to the quasineutral limit for the Vlasov-Poisson equation
• On Quantum Sobolev Inequalities
• Global-in-time Semiclassical Regularity for the Hartree-Fock Equation
• On the $L^2$ Rate of Convergence in the Limit from the Hartree to the Vlasov$\unicode{x2013}$Poisson Equation
• Optimal Semiclassical Regularity of Projection Operators and Strong Weyl Law