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2014 The Hartree equation for infinitely many particles, II: Dispersion and scattering in 2D
Mathieu Lewin, Julien Sabin
Anal. PDE 7(6): 1339-1363 (2014). DOI: 10.2140/apde.2014.7.1339

Abstract

We consider the nonlinear Hartree equation for an interacting gas containing infinitely many particles and we investigate the large-time stability of the stationary states of the form f(Δ), describing a homogeneous quantum gas. Under suitable assumptions on the interaction potential and on the momentum distribution f, we prove that the stationary state is asymptotically stable in dimension 2. More precisely, for any initial datum which is a small perturbation of f(Δ) in a Schatten space, the system weakly converges to the stationary state for large times.

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Mathieu Lewin. Julien Sabin. "The Hartree equation for infinitely many particles, II: Dispersion and scattering in 2D." Anal. PDE 7 (6) 1339 - 1363, 2014. https://doi.org/10.2140/apde.2014.7.1339

Information

Received: 2 October 2013; Accepted: 9 June 2014; Published: 2014
First available in Project Euclid: 20 December 2017

zbMATH: 1301.35122
MathSciNet: MR3270166
Digital Object Identifier: 10.2140/apde.2014.7.1339

Subjects:
Primary: 35Q40

Keywords: Hartree equation , infinite quantum systems , Lindhard function , scattering , Strichartz inequality

Rights: Copyright © 2014 Mathematical Sciences Publishers

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Vol.7 • No. 6 • 2014
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