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Fluctuations of N-particle quantum dynamics around the nonlinear Schrödinger equation


Brennecke, Christian; Nam, Phan Thành; Napiórkowski, Marcin; Schlein, Benjamin (2019). Fluctuations of N-particle quantum dynamics around the nonlinear Schrödinger equation. Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire, 36(5):1201-1235.

Abstract

We consider a system of $N$ bosons interacting through a singular two-body potential scaling with N and having the form $N^{3β-1}V(N^βx)$ , for an arbitrary parameter$β \in(0 ;1)$. We provide a norm-approximation for the many-body evolution of initial data exhibiting Bose–Einstein condensation in terms of a cubic nonlinear Schrödinger equation for the condensate wave function and of a unitary Fock space evolution with a generator quadratic in creation and annihilation operators for the fluctuations.

Abstract

We consider a system of $N$ bosons interacting through a singular two-body potential scaling with N and having the form $N^{3β-1}V(N^βx)$ , for an arbitrary parameter$β \in(0 ;1)$. We provide a norm-approximation for the many-body evolution of initial data exhibiting Bose–Einstein condensation in terms of a cubic nonlinear Schrödinger equation for the condensate wave function and of a unitary Fock space evolution with a generator quadratic in creation and annihilation operators for the fluctuations.

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Additional indexing

Item Type:Journal Article, not_refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Scopus Subject Areas:Physical Sciences > Analysis
Physical Sciences > Mathematical Physics
Physical Sciences > Applied Mathematics
Uncontrolled Keywords:Mathematical Physics, Analysis
Language:English
Date:1 August 2019
Deposited On:23 Jan 2019 15:52
Last Modified:23 Nov 2020 01:00
Publisher:Elsevier
ISSN:0294-1449
OA Status:Green
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1016/j.anihpc.2018.10.007

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