A Quantum Integrable System with Two Colour-Components in Two Dimensions

TL;DR

This paper formulates and solves a two-dimensional quantum integrable system with two colour-components by reducing it to one-dimensional problems and applying Bethe ansatz techniques.

Contribution

It introduces a quantum DS1 system with two colour-components in two dimensions and derives exact solutions using symmetry operators and Bethe ansatz.

Findings

Exact solutions for the quantum DS1 system with two colours

Reduction of 2D problem to solvable 1D many-body problems

Application of Young operators in solving the system

Abstract

The Davey-Stewartson 1(DS1) system[9] is an integrable model in two dimensions. A quantum DS1 system with 2 colour-components in two dimensions has been formulated. This two-dimensional problem has been reduced to two one-dimensional many-body problems with 2 colour-components. The solutions of the two-dimensional problem under consideration has been constructed from the resulting problems in one dimensions. For latters with the $\delta $-function interactions and being solved by the Bethe ansatz, we introduce symmetrical and antisymmetrical Young operators of the permutation group and obtain the exact solutions for the quantum DS1 system. The application of the solusions is discussed.