Perturbation theory and control in classical or quantum mechanics by an inversion formula

@article{Vittot2003PerturbationTA,
  title={Perturbation theory and control in classical or quantum mechanics by an inversion formula},
  author={Michel Vittot},
  journal={Journal of Physics A},
  year={2003},
  volume={37},
  pages={6337-6357}
}
  • M. Vittot
  • Published 2003
  • Physics, Mathematics
  • Journal of Physics A
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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