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.

References in corpus (2)

• One-and-a-half quantum de Finetti theorems
• On quantum estimation, quantum cloning and finite quantum de Finetti theorems

Cited by in corpus (40)

• Optimal Rate for Bose-Einstein Condensation in the Gross-Pitaevskii Regime
• Gross-Pitaevskii Dynamics for Bose-Einstein Condensates
• Complete Bose-Einstein condensation in the Gross-Pitaevskii regime
• Bose-Einstein Condensation Beyond the Gross-Pitaevskii Regime
• Optimal rate of condensation for trapped bosons in the Gross-Pitaevskii regime
• Bose-Einstein Condensation with Optimal Rate for Trapped Bosons in the Gross-Pitaevskii Regime
• Asymptotic expansion of low-energy excitations for weakly interacting bosons
• Excitation Spectrum for Bose Gases beyond the Gross-Pitaevskii Regime
• Bose-Einstein Condensation in a Dilute, Trapped Gas at Positive Temperature
• Local density approximation for the almost-bosonic anyon gas
• Another proof of BEC in the GP-limit
• Gross-Pitaevskii Limit of a Homogeneous Bose Gas at Positive Temperature
• A second order upper bound for the ground state energy of a hard-sphere gas in the Gross-Pitaevskii regime
• The Bose gas in a box with Neumann boundary conditions
• Central Limit Theorem for Bose-Einstein Condensates
• Ground state energy of mixture of Bose gases
• Ground state energy of a Bose gas in the Gross-Pitaevskii regime
• Ground state energy of the low density Bose gas with three-body interactions
• 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
• On Bose-Einstein condensates in the Thomas-Fermi regime
• Exactly solvable Gross-Pitaevskii type equations
• The Excitation Spectrum of the Bose Gas in the Gross-Pitaevskii Regime
• Semiclassical approximation and critical temperature shift for weakly interacting trapped bosons
• A fermionic de Finetti theorem
• Bogoliubov theory for dilute bose gases: the Gross-Pitaevskii Regime
• Upper bound for the grand canonical free energy of the Bose gas in the Gross-Pitaevskii limit for general interaction potentials
• A Short Proof of Bose-Einstein Condensation in the Gross-Pitaevskii Regime and Beyond
• Third order corrections to the ground state energy of a Bose gas in the Gross-Pitaevskii regime
• Many-Body Blow-Up Profile of Boson Stars with External Potentials
• Strong Kac's chaos in the mean-field Bose-Einstein Condensation
• Bose-Einstein condensation on hyperbolic spaces
• The excitation spectrum of a Bose gas with an impurity in the Gross-Pitaevskii regime
• Second Order Expansion of Gibbs State Reduced Density Matrices in the Gross-Pitaevskii Regime
• Effective non-linear spinor dynamics in a spin-1 Bose-Einstein condensate
• Local Density Approximation and Other Limit Regimes for a Homogeneous Bose Gas with Repulsive Three-Body Interactions in Low-Dimensional Space
• A second order upper bound on the ground state energy of a Bose gas beyond the Gross-Pitaevskii regime
• The Low Energy Spectrum of Trapped Bosons in the Gross-Pitaevskii Regime
• Reduced fluctuations for bosons in a double well
• Derivation of the Gross-Pitaevskii Dynamics through Renormalized Excitation Number Operators