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

摘要

We develop some calculation schemes to determine dynamics of a wide class ofintegrable quantum-optical models using their symmetry adapted reformulation interms of polynomial Lie algebras $su_{pd}(2)$. These schemes, based on"diagonal" representations of model evolution operators (via diagonalizingHamiltonians with the help of the $su_{pd}(2)$ defining relations), areimplemented in the form adapted for numerical calculations. Their efficiency isdemonstrated on the example of the second-harmonic-generation model.