Exactly solvable models in atomic and molecular physics

TL;DR

This paper develops exactly solvable models in atomic and molecular physics using algebraic methods, including bosonic and fermionic systems, with solutions obtained via the Bethe ansatz.

Contribution

It systematically constructs integrable models based on the gl(N) and gl(M|N) algebras, extending their applicability to atomic and molecular physics.

Findings

Models related to Bose-Einstein condensates are constructed.

Spectra are obtained analytically using the Bethe ansatz.

Extension to superalgebras includes fermionic systems.

Abstract

We construct integrable generalised models in a systematic way exploring different representations of the gl(N) algebra. The models are then interpreted in the context of atomic and molecular physics, most of them related to different types of Bose-Einstein condensates. The spectrum of the models is given through the analytical Bethe ansatz method. We further extend these results to the case of the superalgebra gl(M|N), providing in this way models which also include fermions.