---
_id: '632'
abstract:
- lang: eng
text: 'We consider a 2D quantum system of N bosons in a trapping potential |x|s,
interacting via a pair potential of the form N2β−1 w(Nβ x). We show that for all
0 < β < (s + 1)/(s + 2), the leading order behavior of ground states of
the many-body system is described in the large N limit by the corresponding cubic
nonlinear Schrödinger energy functional. Our result covers the focusing case (w
< 0) where even the stability of the many-body system is not obvious. This
answers an open question mentioned by X. Chen and J. Holmer for harmonic traps
(s = 2). Together with the BBGKY hierarchy approach used by these authors, our
result implies the convergence of the many-body quantum dynamics to the focusing
NLS equation with harmonic trap for all 0 < β < 3/4. '
author:
- first_name: Mathieu
full_name: Lewin, Mathieu
last_name: Lewin
- first_name: Phan
full_name: Nam, Phan
id: 404092F4-F248-11E8-B48F-1D18A9856A87
last_name: Nam
- first_name: Nicolas
full_name: Rougerie, Nicolas
last_name: Rougerie
citation:
ama: Lewin M, Nam P, Rougerie N. A note on 2D focusing many boson systems. *Proceedings
of the American Mathematical Society*. 2017;145(6):2441-2454. doi:10.1090/proc/13468
apa: Lewin, M., Nam, P., & Rougerie, N. (2017). A note on 2D focusing many boson
systems. *Proceedings of the American Mathematical Society*, *145*(6),
2441–2454. https://doi.org/10.1090/proc/13468
chicago: 'Lewin, Mathieu, Phan Nam, and Nicolas Rougerie. “A Note on 2D Focusing
Many Boson Systems.” *Proceedings of the American Mathematical Society* 145,
no. 6 (2017): 2441–54. https://doi.org/10.1090/proc/13468.'
ieee: M. Lewin, P. Nam, and N. Rougerie, “A note on 2D focusing many boson systems,”
*Proceedings of the American Mathematical Society*, vol. 145, no. 6, pp.
2441–2454, 2017.
ista: Lewin M, Nam P, Rougerie N. 2017. A note on 2D focusing many boson systems.
Proceedings of the American Mathematical Society. 145(6), 2441–2454.
mla: Lewin, Mathieu, et al. “A Note on 2D Focusing Many Boson Systems.” *Proceedings
of the American Mathematical Society*, vol. 145, no. 6, American Mathematical
Society, 2017, pp. 2441–54, doi:10.1090/proc/13468.
short: M. Lewin, P. Nam, N. Rougerie, Proceedings of the American Mathematical Society
145 (2017) 2441–2454.
date_created: 2018-12-11T11:47:36Z
date_published: 2017-01-01T00:00:00Z
date_updated: 2020-01-16T12:38:00Z
day: '01'
department:
- _id: RoSe
doi: 10.1090/proc/13468
intvolume: ' 145'
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1509.09045
month: '01'
oa: 1
oa_version: Submitted Version
page: 2441 - 2454
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Proceedings of the American Mathematical Society
publication_status: published
publisher: American Mathematical Society
publist_id: '7160'
quality_controlled: '1'
status: public
title: A note on 2D focusing many boson systems
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 145
year: '2017'
...