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

2003/03/31 by Michel Vittot · 1 citation
Physics and Astronomy · Mathematics · #math-ph #math.DS #math.MP #math.OC

paper · pdf · doi:10.1088/0305-4470/37/24/011

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

arxiv created 2004/06/07 · arxiv updated 2009/11/30

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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