An implementation of the polynomial Lie algebra methods for solving a class of nonlinear models in quantum optics

V. P. Karassiov; A. A. Gusev; S. I. Vinitsky

paper

An implementation of the polynomial Lie algebra methods for solving a class of nonlinear models in quantum optics

arXiv:quant-ph/0105152

Abstract

We develop some calculation schemes to determine dynamics of a wide class of integrable quantum-optical models using their symmetry adapted reformulation in terms of polynomial Lie algebras $s u_{p d} (2)$ . These schemes, based on "diagonal" representations of model evolution operators (via diagonalizing Hamiltonians with the help of the $s u_{p d} (2)$ defining relations), are implemented in the form adapted for numerical calculations. Their efficiency is demonstrated on the example of the second-harmonic-generation model.

9 pages, LATEX; submitted to Proceedings of XXIII Intternational Colloqium on Group Theoretical Methods in Physics (Dubna, July 31-August 5 2000)