Perturbation Theory and Control in Classical or Quantum Mechanics by an Inversion Formula

Details Perturbation Theory and Control in Classical or Quantum Mechanics by an Inversion Formula Perturbation Theory and Control in Classical or Quantum Mechanics by an Inversion Formula

2003-03-22

arxiv.org/abs/math-ph/0303051v8

Physics

Mathematical Physics

Version 8.0. 26 pages, Latex2e, final version published in J. Phys. A

Scientific paper

10.1088/0305-4470/37/24/011

We consider a perturbation of an ``integrable'' Hamiltonian and give an expression for the canonical or unitary transformation which ``simplifies'' this perturbed system. The problem is to invert a functional defined on the Lie- algebra of observables. We give a bound for the perturbation in order to solve this inversion. And apply this result to a particular case of the control theory, as a first example, and to the ``quantum adiabatic transformation'', as another example.

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