Derivation of Hartree theory for attractive 2D Bose gases

Mathphys Analysis Seminar

In this talk, I will present recent results on two-dimensional Bose gases with attractive interactions. More precisely, I will discuss the validity of Hartree theory, which states that the ground state of the system can be accurately described by an uncorrelated Bose-Einstein condensate. In particular, this means that the ground state energy per particle of the system is well-described by a non-linear Schrdinger energy functional, called the Hartree energy functional. For systems with attractive interactions, this question is particularly non-trivial because the system might not even be stable, meaning that the ground state energy per particle might diverge as the number of particles goes to infinity. As I will explain, there is a sharp threshold on the interaction that determines whether or not the system is stable.
Based on joint work with Lukas Junge.