Derivation of the time dependent two dimensional focusing NLS equation

DOI10.1007/s10955-018-2095-9zbMath1404.35416arXiv1707.06523OpenAlexW2737471677MaRDI QIDQ1990111

Maximilian Jeblick, Peter Pickl

Publication date: 24 October 2018

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.06523

zbMATH Keywords

NLS equationmean-fieldfocusing NLS

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Many-body theory; quantum Hall effect (81V70)

Related Items (12)

The mean-field limit of the Lieb-Liniger model ⋮ Beyond Bogoliubov dynamics ⋮ Norm approximation for many-body quantum dynamics: Focusing case in low dimensions ⋮ Derivation of the 2d Gross-Pitaevskii equation for strongly confined 3d bosons ⋮ Improved stability for 2D attractive Bose gases ⋮ Derivation of the 1d nonlinear Schrödinger equation from the 3d quantum many-body dynamics of strongly confined bosons ⋮ Derivation of the 1d Gross-Pitaevskii equation from the 3d quantum many-body dynamics of strongly confined bosons ⋮ Higher order corrections to the mean-field description of the dynamics of interacting bosons ⋮ Derivation of the time dependent Gross-Pitaevskii equation in two dimensions ⋮ Scaling limits of bosonic ground states, from many-body to non-linear Schrödinger ⋮ Derivation of the Bogoliubov time evolution for a large volume mean-field limit ⋮ Dynamics of large boson systems with attractive interaction and a derivation of the cubic focusing NLS equation in R3

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