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

M. Lewin, P. Nam, N. Rougerie, Transactions of the American Mathematical Society 368 (2016) 6131–6157.


Journal Article | Published | English

Scopus indexed
Author
Lewin, Mathieu; Phan Thanh, NamIST Austria; Rougerie, Nicolas
Department
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.
Publishing Year
Date Published
2016-01-01
Journal Title
Transactions of the American Mathematical Society
Acknowledgement
The authors acknowledge financial support from the European Research Council (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.
Volume
368
Issue
9
Page
6131 - 6157
IST-REx-ID

Cite this

Lewin M, Nam P, Rougerie N. The mean-field approximation and the non-linear Schrödinger functional for trapped Bose gases. Transactions of the American Mathematical Society. 2016;368(9):6131-6157. doi:10.1090/tran/6537
Lewin, M., Nam, P., & Rougerie, N. (2016). The mean-field approximation and the non-linear Schrödinger functional for trapped Bose gases. Transactions of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/tran/6537
Lewin, Mathieu, Phan Nam, and Nicolas Rougerie. “The Mean-Field Approximation and the Non-Linear Schrödinger Functional for Trapped Bose Gases.” Transactions of the American Mathematical Society. American Mathematical Society, 2016. https://doi.org/10.1090/tran/6537.
M. Lewin, P. Nam, and N. Rougerie, “The mean-field approximation and the non-linear Schrödinger functional for trapped Bose gases,” Transactions of the American Mathematical Society, vol. 368, no. 9. American Mathematical Society, pp. 6131–6157, 2016.
Lewin M, Nam P, Rougerie N. 2016. The mean-field approximation and the non-linear Schrödinger functional for trapped Bose gases. Transactions of the American Mathematical Society. 368(9), 6131–6157.
Lewin, Mathieu, et al. “The Mean-Field Approximation and the Non-Linear Schrödinger Functional for Trapped Bose Gases.” Transactions of the American Mathematical Society, vol. 368, no. 9, American Mathematical Society, 2016, pp. 6131–57, doi:10.1090/tran/6537.
All files available under the following license(s):
Copyright Statement:
This Item is protected by copyright and/or related rights. [...]

Link(s) to Main File(s)
Access Level
OA Open Access

Export

Marked Publications

Open Data IST Research Explorer

Search this title in

Google Scholar