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

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

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

Authors

Karassiov, V. P.

Gusev, A. A.

Vinitsky, S. I.

Description

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 $su_{pd}(2)$. These schemes, based on "diagonal" representations of model evolution operators (via diagonalizing Hamiltonians with the help of the $su_{pd}(2)$ 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)