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

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

Quantum Physics 2007-05-23 v1

Authors: V. P. Karassiov , A. A. Gusev , S. I. Vinitsky

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 $su_{pd}(2)$ . 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.

Keywords

polynomial Lie algebras quantum optics integrability second-harmonic generation symmetry adapted Hamiltonian diagonalization

Cite

@article{arxiv.quant-ph/0105152,
  title  = {An implementation of the polynomial Lie algebra methods for solving a class of nonlinear models in quantum optics},
  author = {V. P. Karassiov and A. A. Gusev and S. I. Vinitsky},
  journal= {arXiv preprint arXiv:quant-ph/0105152},
  year   = {2007}
}

Comments

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

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

Abstract

Keywords

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