From the Hartree dynamics to the Vlasov equation

Niels Patriz Benedikter; Marcello  Porta; Chiara  Saffirio; Benjamin Schlein

doi:10.1007/s00205-015-0961-z

From the Hartree dynamics to the Vlasov equation

Niels Patriz Benedikter, Marcello Porta, Chiara Saffirio, Benjamin Schlein

Department of Mathematical Sciences

21 Citations (Scopus)

119 Downloads (Pure)

Abstract

We consider the evolution of quasi-free states describing N fermions in the mean field limit, as governed by the nonlinear Hartree equation. In the limit of large 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.

Original language	English
Journal	Archive for Rational Mechanics and Analysis
Volume	221
Issue number	1
Pages (from-to)	273–334
ISSN	0003-9527
DOIs	https://doi.org/10.1007/s00205-015-0961-z
Publication status	Published - 1 Jul 2016

Access to Document

10.1007/s00205-015-0961-z

Feom the HartreeAccepted author manuscript, 465 KB

Cite this

@article{46ec969dc0e346e4833d92d4e4276883,

title = "From the Hartree dynamics to the Vlasov equation",

abstract = "We consider the evolution of quasi-free states describing N fermions in the mean field limit, as governed by the nonlinear Hartree equation. In the limit of large 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.",

author = "Benedikter, {Niels Patriz} and Marcello Porta and Chiara Saffirio and Benjamin Schlein",

year = "2016",

month = jul,

day = "1",

doi = "10.1007/s00205-015-0961-z",

language = "English",

volume = "221",

pages = "273–334",

journal = "Archive for Rational Mechanics and Analysis",

issn = "0003-9527",

publisher = "Springer",

number = "1",

}

TY - JOUR

T1 - From the Hartree dynamics to the Vlasov equation

AU - Benedikter, Niels Patriz

AU - Porta, Marcello

AU - Saffirio, Chiara

AU - Schlein, Benjamin

PY - 2016/7/1

Y1 - 2016/7/1

N2 - We consider the evolution of quasi-free states describing N fermions in the mean field limit, as governed by the nonlinear Hartree equation. In the limit of large 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.

AB - We consider the evolution of quasi-free states describing N fermions in the mean field limit, as governed by the nonlinear Hartree equation. In the limit of large 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.

U2 - 10.1007/s00205-015-0961-z

DO - 10.1007/s00205-015-0961-z

M3 - Journal article

SN - 0003-9527

VL - 221

SP - 273

EP - 334

JO - Archive for Rational Mechanics and Analysis

JF - Archive for Rational Mechanics and Analysis

IS - 1

ER -

From the Hartree dynamics to the Vlasov equation

Abstract

Access to Document

Fingerprint

Cite this