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Ground states of large
bosonic systems: the Gross–Pitaevskii limit revisited
Phan Thành Nam, Nicolas Rougerie and Robert Seiringer |
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Vol. 9 (2016), No. 2, 459–485
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Abstract |
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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. |
Keywords
many-body quantum mechanics, mean-field limits,
Bose–Einstein condensates
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Mathematical Subject Classification 2010
Primary: 35Q40, 81V70
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Milestones
Received: 30 April 2015
Revised: 8 September 2015
Accepted: 6 January 2016
Published: 24 March 2016
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Authors |
| Phan Thành Nam | |
| Institute of Science and Technology
Austria Am Campus 1 3400 Klosterneuburg Austria |
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| 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 France |
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| Robert Seiringer | |
| Institute of Science and Technology
Austria Am Campus 1 3400 Klosterneuburg Austria |
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