Author(s):

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

Article Title: 
A note on 2D focusing many boson systems

Affiliation 
IST Austria 
Abstract: 
We consider a 2D quantum system of N bosons in a trapping potential xs, 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 manybody 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 manybody 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 manybody quantum dynamics to the focusing NLS equation with harmonic trap for all 0 < β < 3/4.

Journal Title:

Proceedings of the American Mathematical Society

Volume: 
145

Issue 
6

ISSN:

10886826

Publisher:

American Mathematical Society

Date Published:

20170101

Start Page: 
2441

End Page:

2454

Sponsor: 
The authors acknowledge financial support from the European Union?s Seventh Framework Programme (ERC Grant MNIQS no. 258023 and REA Grant no. 291734) and the ANR (Mathostaq Project ID ANR13JS01000501).

URL: 

DOI: 
10.1090/proc/13468

Open access: 
yes (repository) 