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Article Dans Une Revue Journal of Physics A: Mathematical and Theoretical Année : 2004

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

Résumé

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.

Dates et versions

hal-00021319 , version 1 (21-03-2006)

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Michel Vittot. Perturbation Theory and Control in Classical or Quantum Mechanics by an Inversion Formula. Journal of Physics A: Mathematical and Theoretical, 2004, 37, pp.6337-6357. ⟨hal-00021319⟩
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