Propagation of Moments and Semiclassical Limit from Hartree to Vlasov Equation

Abstract

In this paper, we prove a quantitative version of the semiclassical limit from the Hartree to the Vlasov equation with singular interaction, including the Coulomb potential. To reach this objective, we also prove the propagation of velocity moments and weighted Schatten norms which implies the boundedness of the space density of particles uniformly in the Planck constant.

arXiv comment42 pages, typos added, clarifications of hypotheses in theorems 3 and 4 and missing sup_{[0,T]} added

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Cited by in corpus (12)

• Combined mean-field and semiclassical limits of large fermionic systems
• Global Semiclassical Limit from Hartree to Vlasov Equation for Concentrated Initial Data
• A new perspective on Wasserstein distances for kinetic problems
• 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
• Convergence towards the Vlasov-Poisson Equation from the $N$-Fermionic Schrödinger Equation
• A mixed-norm estimate of the two-particle reduced density matrix of many-body Schrödinger dynamics for deriving the Vlasov equation
• Propagation of moments for large data and semiclassical limit to the relativistic Vlasov equation
• Uniqueness criteria for the Vlasov--Poisson system and applications to semiclassical analysis
• Effective Dynamics of Interacting Fermions from Semiclassical Theory to the Random Phase Approximation
• Enhanced Stability in Quantum Optimal Transport Pseudometrics: From Hartree to Vlasov-Poisson