Dilute Bose gas with three-body interaction: recent results and open questions

TL;DR

This paper reviews recent findings on the ground state energy of dilute Bose gases with three-body interactions, highlighting the emergence of a 3D energy-critical Schrödinger equation and discussing open questions.

Contribution

It introduces a novel description of the ground state energy using a 3D energy-critical Schrödinger equation linked to three-body interactions.

Findings

Emergence of a 3D energy-critical Schrödinger equation for the ground state energy

Ground state energy determined by a zero scattering problem

Discussion of open questions in the field

Abstract

We review our recent study on the ground state energy of dilute Bose gases with three-body interactions. The main feature of our results is the emergence of the 3D energy-critical Schr\"odinger equation to describe the ground state energy of a Bose-Einstein condensate, where the nonlinearity strength is determined by a zero scattering problem. Several open questions will also be discussed.