Enhanced Stability in Quantum Optimal Transport Pseudometrics: From Hartree to Vlasov-Poisson
Analysis of PDEs
2024-12-02 v1 Mathematical Physics
math.MP
Quantum Physics
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.
Keywords
Cite
@article{arxiv.2401.05773,
title = {Enhanced Stability in Quantum Optimal Transport Pseudometrics: From Hartree to Vlasov-Poisson},
author = {Mikaela Iacobelli and Laurent Lafleche},
journal= {arXiv preprint arXiv:2401.05773},
year = {2024}
}
Comments
18 pages