Ground states of large bosonic systems: The gross-pitaevskii limit revisited

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 non-linear 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.

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• Excitation Spectrum for Bose Gases beyond the Gross-Pitaevskii Regime
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• Upper bound for the grand canonical free energy of the Bose gas in the Gross-Pitaevskii limit
• Dilute Bose gas with three-body interaction: recent results and open questions
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• Many-Body Blow-Up Profile of Boson Stars with External Potentials
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• The excitation spectrum of a Bose gas with an impurity in the Gross-Pitaevskii regime
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• Local Density Approximation and Other Limit Regimes for a Homogeneous Bose Gas with Repulsive Three-Body Interactions in Low-Dimensional Space
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• The Low Energy Spectrum of Trapped Bosons in the Gross-Pitaevskii Regime
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