Why a System of Three Bosons on Separate Lines Can Not Exhibit the Confinement Induced Efimov Effect

TL;DR

This paper rigorously disproves the prediction that a three-boson system constrained on three lines exhibits the Efimov effect, demonstrating instead that it has only finitely many bound states.

Contribution

The paper provides a mathematical proof that the confinement induced Efimov effect does not occur in this specific three-line boson system.

Findings

The system has at most finitely many bound states.

The predicted Efimov effect does not occur in this configuration.

Mathematical proof refutes previous physics predictions.

Abstract

We study a system of three bosons interacting with short-range potentials which can move along three different lines. Two of these lines are parallel to each other within one plane. The third line is constrained to a plane perpendicular to the first one. Recently it was predicted in physics literature that such a system exhibits the so-called confinement induced Efimov effect. We prove that this prediction is not correct by showing that this system has at most finitely many bound-states.