Author(s):

Lewin, Mathieu; Nam, Phan Thanh; Rougerie, Nicolas

Article Title: 
The meanfield approximation and the nonlinear Schrödinger functional for trapped Bose gases

Affiliation 
IST Austria 
Abstract: 
We study the ground state of a trapped Bose gas, starting from the full manybody Schrödinger Hamiltonian, and derive the nonlinear Schrödinger energy functional in the limit of a large particle number, when the interaction potential converges slowly to a Dirac delta function. Our method is based on quantitative estimates on the discrepancy between the full manybody energy and its meanfield approximation using Hartree states. These are proved using finite dimensional localization and a quantitative version of the quantum de Finetti theorem. Our approach covers the case of attractive interactions in the regime of stability. In particular, our main new result is a derivation of the 2D attractive nonlinear Schrödinger ground state.

Journal Title:

Transactions of the American Mathematical Society

Volume: 
368

Issue 
9

ISSN:

10886850

Publisher:

American Mathematical Society

Date Published:

20160101

Start Page: 
6131

End Page:

6157

URL: 

DOI: 
10.1090/tran/6537

Notes: 
The authors acknowledge financial support from the European Research Coun
cil (FP7/20072013 Grant Agreement MNIQS 258023) and the ANR (Mathostaq
project, ANR13JS01000501). The second and third authors have benefited from
the hospitality of the Institute for Mathematical Science of the National University
of Singapore.

Open access: 
yes (repository) 