Derivation of the 3D quintic Gross--Pitaevskii equation

TL;DR

This paper proves that Bose--Einstein condensates with three-body interactions in three dimensions evolve according to a universal quintic Gross--Pitaevskii equation, preserving condensation and linking the effective coupling to a three-body scattering hypervolume.

Contribution

It rigorously derives the energy-critical quintic Gross--Pitaevskii equation for three-body interactions in 3D Bose--Einstein condensates, establishing universality of the coupling constant.

Findings

Condensation is preserved under many-body evolution.

The condensate wavefunction follows the quintic Gross--Pitaevskii equation.

The effective coupling depends only on the three-body scattering hypervolume.

Abstract

We study the time evolution of Bose--Einstein condensates with three-body interactions in the Gross--Pitaevskii regime. We show that Bose--Einstein condensation is preserved under many-body evolution and that the condensate wavefunction evolves according to the quintic Gross--Pitaevskii equation in $\mathbb{R}^3$, which is energy critical. In particular, we show that the effective coupling constant is universal and depends only on a three-body scattering hypervolume.