A note on 2D focusing many boson systems Journal Article

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 |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.
Journal Title: Proceedings of the American Mathematical Society
Volume: 145
Issue 6
ISSN: 1088-6826
Publisher: American Mathematical Society  
Date Published: 2017-01-01
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 ANR-13-JS01-0005-01).
DOI: 10.1090/proc/13468
Open access: yes (repository)
IST Austria Authors
  1. Phan Thanh Nam
    12 Nam