A note on 2D focusing many boson systems

M. Lewin, P. Nam, N. Rougerie, Proceedings of the American Mathematical Society 145 (2017) 2441–2454.


Journal Article | Published | English
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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.
Publishing Year
Date Published
2017-01-01
Journal Title
Proceedings of the American Mathematical Society
Volume
145
Issue
6
Page
2441 - 2454
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Cite this

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
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
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.
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.
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.
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.

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