Abstract
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.
Citation
Phan Thánh Nam. Nicolas Rougerie. Robert Seiringer. "Ground states of large bosonic systems: the Gross–Pitaevskii limit revisited." Anal. PDE 9 (2) 459 - 485, 2016. https://doi.org/10.2140/apde.2016.9.459
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