Lewin, Mathieu; Sabin, Julien The Hartree equation for infinitely many particles. II: Dispersion and scattering in 2D. (English) Zbl 1301.35122 Anal. PDE 7, No. 6, 1339-1363 (2014). Summary: 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 \(f(-\Delta)\), 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 \(f(-\Delta)\) in a Schatten space, the system weakly converges to the stationary state for large times. For part I, see [the authors, arXiv:1310.0603, to appear in Commun Math. Phys., doi:10.1007/s00220-014-2098-6]. Cited in 2 ReviewsCited in 31 Documents MSC: 35Q40 PDEs in connection with quantum mechanics 82C22 Interacting particle systems in time-dependent statistical mechanics 35B35 Stability in context of PDEs Keywords:Hartree equation; infinite quantum systems; Strichartz inequality; scattering; Lindhard function PDFBibTeX XMLCite \textit{M. Lewin} and \textit{J. Sabin}, Anal. PDE 7, No. 6, 1339--1363 (2014; Zbl 1301.35122) Full Text: DOI arXiv References: This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.