Perturbation Theory and Control in Classical or Quantum Mechanics by an Inversion Formula
Vittot, Michel
HAL, hal-00021319 / Harvested from HAL
Text on HAL
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.
Publié le : 2004-07-05
Classification:  [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph],  [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph],  [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS],  [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] 
@article{hal-00021319,
     author = {Vittot, Michel},
     title = {Perturbation Theory and Control in Classical or Quantum Mechanics by an Inversion Formula},
     journal = {HAL},
     volume = {2004},
     number = {0},
     year = {2004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00021319}
}

Vittot, Michel. Perturbation Theory and Control in Classical or Quantum Mechanics by an Inversion Formula. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00021319/