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.
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