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Perturbation Theory and Control in Classical or Quantum Mechanics by an Inversion Formula | | Michel Vittot
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22 Mar 2003 | | Subject: | Mathematical Physics; Dynamical Systems; Optimization and Control | math-ph math.DS math.MP math.OC | | Affiliation: | Centre de Physique Theorique, CNRS Luminy, Marseille, France | | 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. | | Source: | arXiv, math-ph/0303051 | | Services: | Forum | Review | PDF | Favorites | |
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