From three-body resonances to bound states in a continuum: pole trajectories

TL;DR

This paper explores how three-body bound states in the continuum (BIC) form by analyzing pole trajectories in a one-dimensional model, revealing their dependence on system parameters like interaction strength, range, and mass ratio.

Contribution

It systematically characterizes the parametric conditions for three-body BIC formation and extends understanding of their sensitivity to kinematic factors over interaction details.

Findings

At least one three-body BIC can form through parameter variation.

Mass ratio changes produce multiple BIC locations with regular patterns.

BIC formation is more influenced by kinematic structure than interaction specifics.

Abstract

We investigate the formation of three-body bound states in the continuum by tracing pole trajectories in the complex energy plane under variation of system parameters. Using a one-dimensional model of two identical bosons and a distinguishable particle interacting via Gaussian potentials, we systematically vary the interaction strength, interaction range, and mass ratio. Our results confirm the parametric nature of few-body bound states in a continuum (BIC) and extend this characterization to a broader set of system parameters. Specifically, we find that variations of both interaction parameters and the mass ratio can lead to the formation of at least one three-body BIC. However, the exact shape of trajectories differs, and for the mass ratio variation we find a more regular pattern with multiple BIC locations. These results suggest that the mechanism of few-body BIC formation is more sensitive to the kinematic structure of the problem than to the specific details of the two-body interaction.