Solvable models of Bose-Einstein condensates: a new algebraic Bethe ansatz scheme

TL;DR

This paper introduces a novel algebraic Bethe ansatz approach using Z-graded representations of the Yang-Baxter algebra to solve models describing Bose-Einstein condensates.

Contribution

It presents a new algebraic Bethe ansatz scheme specifically designed for integrable models of Bose-Einstein condensates, expanding the mathematical toolkit for these systems.

Findings

Developed a Z-graded representation framework

Successfully diagonalized relevant integrable models

Enhanced understanding of algebraic structures in BEC models

Abstract

A new algebraic Bethe ansatz scheme is proposed to diagonalise classes of integrable models relevant to the description of Bose-Einstein condensates in dilute alkali gases. This is achieved by introducing the notion of Z-graded representations of the Yang-Baxter algebra.