Green's Functions and the Adiabatic Hyperspherical Method

TL;DR

This paper develops a comprehensive framework using Green's functions and the adiabatic hyperspherical method to analyze few-body quantum systems, providing new semi-analytic solutions and a model for atom-loss in ultracold gases.

Contribution

It derives a general hyperangular Green's function in d-dimensions and applies it to three-particle systems with zero-range interactions, including a model for atom-loss in ultracold gases.

Findings

Derived a general hyperangular Green's function in d-dimensions.

Solved the Lippmann-Schwinger equation for three particles with zero-range interactions.

Presented a model for atom-loss due to three-body recombination in ultracold gases.

Abstract

We address the few-body problem using the adiabatic hyperspherical representation. A general form for the hyperangular Green's function in $d$-dimensions is derived. The resulting Lippmann-Schwinger equation is solved for the case of three-particles with s-wave zero-range interactions. Identical particle symmetry is incorporated in a general and intuitive way. Complete semi-analytic expressions for the nonadiabatic channel couplings are derived. Finally, a model to describe the atom-loss due to three-body recombination for a three-component fermi-gas of $^{6}$Li atoms is presented.