Stability and correlations in dilute two-dimensional boson systems

TL;DR

This paper uses the hyperspherical adiabatic expansion method to analyze correlations and stability in two-dimensional boson systems, revealing conditions for instability and connections to known quantum effects.

Contribution

It provides a rigorous analysis of correlations in 2D boson systems and derives stability conditions related to the Thomas and Efimov effects.

Findings

Instability occurs at specific attractive potential strengths.

Hyperangular eigenvalues are nearly independent of hyperradius.

Stability conditions resemble mean-field criteria.

Abstract

The hyperspherical adiabatic expansion method is used to describe correlations in a symmetric boson system rigorously confined to two spatial dimensions. The hyperangular eigenvalue equation turns out to be almost independent of the hyperradius, whereas the solutions are strongly varying with the strength of the attractive two-body potentials. Instability is encountered in hyperangular, hyperradial, and mean-field equations for almost identical strengths inversely proportional to the particle number. The derived conditions for stability are similar to mean-field conditions and closely related to the possible occurrence of the Thomas and Efimov effects. Renormalization in mean-field calculations for two spatial dimensions is probably not needed.