Vol. 9, No. 2, 2016

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Ground states of large bosonic systems: the Gross–Pitaevskii limit revisited

Phan Thành Nam, Nicolas Rougerie and Robert Seiringer

Vol. 9 (2016), No. 2, 459–485

We study the ground state of a dilute Bose gas in a scaling limit where the Gross–Pitaevskii functional emerges. This is a repulsive nonlinear Schrödinger functional whose quartic term is proportional to the scattering length of the interparticle interaction potential. We propose a new derivation of this limit problem, with a method that bypasses some of the technical difficulties that previous derivations had to face. The new method is based on a combination of Dyson’s lemma, the quantum de Finetti theorem and a second moment estimate for ground states of the effective Dyson Hamiltonian. It applies equally well to the case where magnetic fields or rotation are present.

many-body quantum mechanics, mean-field limits, Bose–Einstein condensates
Mathematical Subject Classification 2010
Primary: 35Q40, 81V70
Received: 30 April 2015
Revised: 8 September 2015
Accepted: 6 January 2016
Published: 24 March 2016
Phan Thành Nam
Institute of Science and Technology Austria
Am Campus 1
3400 Klosterneuburg
Nicolas Rougerie
Université Grenoble 1 and Centre National de la Recherche Scientifique
Laboratoire de Physique et Modélisation des Milieux Condensés (UMR 5493)
BP 166
38042 Grenoble
Robert Seiringer
Institute of Science and Technology Austria
Am Campus 1
3400 Klosterneuburg