An numerical approach for finite volume three-body interaction

TL;DR

This paper develops a numerical method to analyze three-body interactions in a finite volume, validated against exact solutions for a simplified one-dimensional model with pairwise delta-function potentials.

Contribution

It introduces a novel numerical approach for finite volume three-body problems and demonstrates its effectiveness through comparison with exact solutions in a toy model.

Findings

Numerical results agree well with exact solutions.

The method effectively handles pairwise delta-function interactions.

Provides a new tool for studying three-body systems in finite volumes.

Abstract

In present work, we study an numerical approach to one dimensional finite volume three-body interaction, the method is demonstrated by considering a toy model of three spinless particles interacting with pair-wise $\delta$-function potentials. The numerical results are compared with the exact solutions of three spinless bosons interaction when strength of short-range interactions are set equal for all pairs.