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From the Hartree dynamics to the Vlasov equation


Benedikter, Niels; Porta, Marcello; Saffirio, Chiara; Schlein, Benjamin (2016). From the Hartree dynamics to the Vlasov equation. Archiv for Rational Mechanics and Analysis, 221(1):273-334.

Abstract

We consider the evolution of quasi-free states describing $\mathit{N}$ fermions in the mean field limit, as governed by the nonlinear Hartree equation. In the limit of large $\mathit{N}$, we study the convergence towards the classical Vlasov equation. For a class of regular interaction potentials, we establish precise bounds on the 0rate of convergence.

Abstract

We consider the evolution of quasi-free states describing $\mathit{N}$ fermions in the mean field limit, as governed by the nonlinear Hartree equation. In the limit of large $\mathit{N}$, we study the convergence towards the classical Vlasov equation. For a class of regular interaction potentials, we establish precise bounds on the 0rate of convergence.

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Additional indexing

Item Type:Journal Article, not refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:January 2016
Deposited On:01 Feb 2017 11:09
Last Modified:03 Feb 2017 01:00
Publisher:Springer
ISSN:0003-9527
Publisher DOI:https://doi.org/10.1007/s00205-015-0961-z

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