10.1090/proc/13468
Lewin, Mathieu
Mathieu
Lewin
Nam, Phan
Phan
Nam
Rougerie, Nicolas
Nicolas
Rougerie
A note on 2D focusing many boson systems
American Mathematical Society
2017
2018-12-11T11:47:36Z
2020-01-16T12:38:00Z
journal_article
https://research-explorer.app.ist.ac.at/record/632
https://research-explorer.app.ist.ac.at/record/632.json
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.