Improved stability for 2D attractive Bose gases

TL;DR

This paper improves the stability conditions for 2D attractive Bose gases, showing that the many-body ground states and dynamics more reliably converge to the mean-field NLS description in dilute regimes.

Contribution

It extends the range of diluteness parameters for which stability and convergence to the NLS are proven in 2D attractive Bose gases.

Findings

Enhanced stability conditions for 2D attractive Bose gases.

Proved convergence of many-body ground states to NLS solutions.

Extended the validity of mean-field approximation in dilute regimes.

Abstract

We study the ground-state energy of N attractive bosons in the plane. The interaction is scaled for the gas to be dilute, so that the corresponding mean-field problem is a local non-linear Schr{\"o}dinger (NLS) equation. We improve the conditions under which one can prove that the many-body problem is stable (of the second kind). This implies, using previous results, that the many-body ground states and dynamics converge to the NLS ones for an extended range of diluteness parameters.