Universal Properties of Two-Dimensional Boson Droplets

TL;DR

This paper investigates the universal properties of two-dimensional boson droplets, revealing energy ratios and bound state characteristics for large N boson systems with weak short-range attraction.

Contribution

It demonstrates the universality of N-boson bound states in 2D and provides precise energy ratios and bound state counts, extending understanding of few-body quantum systems.

Findings

Energy ratio B_{N+1}/B_N approaches ~8.567 for large N.

Three-body system has exactly two bound states.

Precise ground and excited state energies for three bosons.

Abstract

We consider a system of N nonrelativistic bosons in two dimensions, interacting weakly via a short-range attractive potential. We show that for N large, but below some critical value, the properties of the N-boson bound state are universal. In particular, the ratio of the binding energies of (N+1)- and N-boson systems, B_{N+1}/B_N, approaches a finite limit, approximately 8.567, at large N. We also confirm previous results that the three-body system has exactly two bound states. We find for the ground state B_3^(0) = 16.522688(1) B_2 and for the excited state B_3^(1) = 1.2704091(1) B_2.