 98539 Asch, J., Duclos, P. and Exner, P.
 Stability of driven systems with growing gaps,
Quantum rings and Wannier ladders
(42K, latex2e)
Jul 23, 98

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Abstract. We consider a quantum particle in a periodic
structure submitted to a constant external electromotive force. The
periodic background is given by a smooth potential plus singular
point interactions and has the property that the gaps between its bands
are growing with the band index. We prove that the
spectrum is pure pointi.e. trajectories of wave packets lie in
compact sets in Hilbert space if the Bloch frequency is nonresonant
with the frequency of the system and satisfies a Diophantine
type estimate, or if it is resonant. Furthermore it
is shown that the KAM method employed in the nonresonant case
produces uniform bounds on the growth of energy for driven systems.
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