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

Michel Vittot
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Abstract

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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BibTeXRIS

Michel Vittot. 2004-06-07. Perturbation Theory and Control in Classical or Quantum Mechanics by an Inversion Formula. https://doi.org/10.1088/0305-4470/37/24/011

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