Analysis of Lyapunov Control for Hamiltonian Quantum Systems

Details Analysis of Lyapunov Control for Hamiltonian Quantum Systems Analysis of Lyapunov Control for Hamiltonian Quantum Systems

2008-05-19

arxiv.org/abs/0805.2882v1

Proceedings of ENOC 2008 (St Petersburg, Russia, June 30-July 4, 2008), http://lib.physcon.ru/?item=1761

Physics

Quantum Physics

7 pages, no figures, mainly a concise summary of 0701.0702

Scientific paper

We present detailed analysis of the convergence properties and effectiveness of Lyapunov control design for bilinear Hamiltonian quantum systems based on the application of LaSalle's invariance principle and stability analysis from dynamical systems and control theory. For a certain class of Hamiltonians, strong convergence results can be obtained for both pure and mixed state systems. The control Hamiltonians for realistic physical systems, however, generally do not fall in this class. It is shown that the effectiveness of Lyapunov control design in this case is significantly diminished.

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