One-dimensional ultracold atomic gases: Impact of the effective range on integrability

TL;DR

This paper investigates how finite effective range affects the integrability of one-dimensional ultracold atomic gases, revealing non-integrability and specific wave function continuity conditions that challenge traditional contact models.

Contribution

It introduces a two-channel model to demonstrate non-integrability in systems with finite effective range and clarifies the wave function behavior at three-particle contact points.

Findings

Systems are not integrable with finite effective range.

Wave functions satisfy specific continuity conditions.

Deviations from Bethe ansatz predictions near integrability.

Abstract

Three identical bosons or fermions are considered in the limit of zero-range interactions and finite effective range. By using a two channel model, we show that these systems are not integrable and that the wave function verifies specific continuity conditions at the contact of three particles. This last feature permits us to solve a contradiction brought by the contact model which can lead to an opposite result concerning the integrability issue. For fermions, the vicinity of integrability is characterized by large deviations with respect to the predictions of the Bethe ansatz.