A supercircle description of universal three-body states in two dimensions

TL;DR

This paper investigates universal three-body bound states in two-dimensional systems, revealing how energy ratios and mass ratios determine the energy spectrum and introducing a supercircle model to describe these states.

Contribution

It introduces a supercircle-based equation to relate three-body and two-body energies in 2D systems, providing a predictive relation for universal three-body energies.

Findings

Energy ratios and mass ratios fully characterize three-body energies.

The supercircle radius increases linearly with three-body energy.

A simple relation predicts universal three-body energies based on system parameters.

Abstract

We consider bound states of asymmetric three-body systems confined to two dimensions. In the universal regime, two energy ratios and two mass ratios provide complete knowledge of the three-body energy measured in units of one two-body energy. The lowest number of stable bound states is produced when one mass is larger than two similar masses. We focus on selected asymmetric systems of interest in cold atom physics. The scaled three-body energy and the two scaled two-body energies are related through an equation for a supercircle whose radius increases almost linearly with three-body energy. The exponents exhibit an increasing behavior with three-body energy. The mass dependence is highly non-trivial. We give a simple relation that predicts the universal three-body energy.