Chaotic Behaviour in Quantum Dynamics.

摘要

Since the classical chaotic diffusion provides a very efficient route to ionization, it is interesting to investigate how the quantum delocalization border can be possibly lowered. In view of the above quoted similarity of the dynamical localization phenomenon for periodically perturbed quantum systems with the Anderson localization phenomenon for a random potential, one would expect that, in order to make localization less effective, the dynamical counterpart of a discrete lattice of dimension higher than one should be considered. A straightforward way to do so would seem just to consider a two dimensional model for a highly excited hydrogen atom in a microwave field. On the other hand,the correspondence between dynamical and Anderson localization was derived and analyzed for the special case of the kicked rotator. Even though our extrapolation of results obtained for the rotator model to the hydrogen atom problem was fully justified by results of numerical simulation, a closer theoretical analysis to be necessary in order that the actual relevance of localization theory for the problem of microwave ionization might be assessed. (jhd)