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The Hartree equation
for infinitely many particles, II: Dispersion and scattering
in 2D
Mathieu Lewin and Julien Sabin |
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Vol. 7 (2014), No. 6, 1339–1363
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Abstract |
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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 , describing a homogeneous quantum gas. Under suitable assumptions on the interaction potential and on the momentum distribution , we prove that the stationary state is asymptotically stable in dimension 2. More precisely, for any initial datum which is a small perturbation of in a Schatten space, the system weakly converges to the stationary state for large times. |
Keywords
Hartree equation, infinite quantum systems, Strichartz
inequality, scattering, Lindhard function
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Mathematical Subject Classification 2010
Primary: 35Q40
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Milestones
Received: 2 October 2013
Accepted: 9 June 2014
Published: 18 October 2014
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Authors |
| Mathieu Lewin | |
| CNRS & Université de
Cergy-Pontoise Mathematics Department UMR 8088 F-95000 Cergy-Pontoise France |
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| Julien Sabin | |
| Université de Cergy-Pontoise Mathematics Department UMR 8088 F-95000 Cergy-Pontoise France |
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