Instabilities in the Mean Field Limit

Daniel Han-Kwan; Toan T. Nguyen

doi:10.1007/s10955-016-1455-6

Instabilities in the Mean Field Limit

Daniel Han-Kwan, Toan T. Nguyen

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

Consider a system of N particles interacting through Newton’s second law with Coulomb interaction potential in one spatial dimension or a (Formula presented.) smooth potential in any dimension. We prove that in the mean field limit (Formula presented.) , the N particles system displays instabilities in times of order (Formula presented.) , for some configurations approximately distributed according to unstable homogeneous equilibria.

Original language	English (US)
Pages (from-to)	1639-1653
Number of pages	15
Journal	Journal of Statistical Physics
Volume	162
Issue number	6
DOIs	https://doi.org/10.1007/s10955-016-1455-6
State	Published - Mar 1 2016

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s10955-016-1455-6

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title = "Instabilities in the Mean Field Limit",

abstract = "Consider a system of N particles interacting through Newton{\textquoteright}s second law with Coulomb interaction potential in one spatial dimension or a (Formula presented.) smooth potential in any dimension. We prove that in the mean field limit (Formula presented.) , the N particles system displays instabilities in times of order (Formula presented.) , for some configurations approximately distributed according to unstable homogeneous equilibria.",

author = "Daniel Han-Kwan and Nguyen, {Toan T.}",

note = "Funding Information: The first author thanks Maxime Hauray and Fr{\'e}d{\'e}ric Rousset for stimulating discussions. We are also grateful to Maxime Hauray for explaining to us how to build N particles global flows in the one-dimensional coulombian case. We finally thank the anonymous referees for several insightful comments and suggestions about this work. TN was supported in part by the NSF under Grant DMS-1405728. Publisher Copyright: {\textcopyright} 2016, Springer Science+Business Media New York.",

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T1 - Instabilities in the Mean Field Limit

AU - Han-Kwan, Daniel

AU - Nguyen, Toan T.

N1 - Funding Information: The first author thanks Maxime Hauray and Frédéric Rousset for stimulating discussions. We are also grateful to Maxime Hauray for explaining to us how to build N particles global flows in the one-dimensional coulombian case. We finally thank the anonymous referees for several insightful comments and suggestions about this work. TN was supported in part by the NSF under Grant DMS-1405728. Publisher Copyright: © 2016, Springer Science+Business Media New York.

PY - 2016/3/1

Y1 - 2016/3/1

N2 - Consider a system of N particles interacting through Newton’s second law with Coulomb interaction potential in one spatial dimension or a (Formula presented.) smooth potential in any dimension. We prove that in the mean field limit (Formula presented.) , the N particles system displays instabilities in times of order (Formula presented.) , for some configurations approximately distributed according to unstable homogeneous equilibria.

AB - Consider a system of N particles interacting through Newton’s second law with Coulomb interaction potential in one spatial dimension or a (Formula presented.) smooth potential in any dimension. We prove that in the mean field limit (Formula presented.) , the N particles system displays instabilities in times of order (Formula presented.) , for some configurations approximately distributed according to unstable homogeneous equilibria.

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SP - 1639

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JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

IS - 6

ER -

Instabilities in the Mean Field Limit

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