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

TL;DR

This paper revisits the derivation of the Gross-Pitaevskii limit for dilute Bose gases, introducing a new method that simplifies the process and applies to more general conditions including magnetic fields and rotation.

Contribution

A novel derivation of the Gross-Pitaevskii limit using Dyson's lemma, quantum de Finetti theorem, and second moment estimates, applicable to magnetic fields and rotation.

Findings

New derivation simplifies previous methods.

Method applies to systems with magnetic fields or rotation.

Validates the emergence of the Gross-Pitaevskii functional in dilute Bose gases.

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 Schr\"odinger 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.