Journal
ANALYSIS & PDE
Volume 9, Issue 2, Pages 459-485Publisher
MATHEMATICAL SCIENCE PUBL
DOI: 10.2140/apde.2016.9.459
Keywords
many-body quantum mechanics; mean-field limits; Bose-Einstein condensates
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Funding
- European Union's Seventh Framework Programme [291734]
- ANR (MaThoStaQ project) [ANR-13-JS01-0005-01]
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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 Schrodinger 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.
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