The mean-field approximation and the non-linear Schrödinger functional for trapped Bose gases Journal Article


Author(s): Lewin, Mathieu; Nam, Phan Thanh; Rougerie, Nicolas
Article Title: The mean-field approximation and the non-linear Schrödinger functional for trapped Bose gases
Affiliation IST Austria
Abstract: We study the ground state of a trapped Bose gas, starting from the full many-body Schrödinger Hamiltonian, and derive the non-linear 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 many-body energy and its mean-field 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 non-linear Schrödinger ground state.
Journal Title: Transactions of the American Mathematical Society
Volume: 368
Issue 9
ISSN: 1088-6850
Publisher: American Mathematical Society  
Date Published: 2016-01-01
Start Page: 6131
End Page: 6157
URL:
DOI: 10.1090/tran/6537
Notes: The authors acknowledge financial support from the European Research Coun- cil (FP7/2007-2013 Grant Agreement MNIQS 258023) and the ANR (Mathostaq project, ANR-13-JS01-0005-01). 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)
IST Austria Authors
  1. Phan Thanh Nam
    12 Nam
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