 02167 O.Bourget
 Singular Continuous Floquet Operator for Systems with Increasing Gaps
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Apr 4, 02

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Abstract. Consider the Floquet operator of a time independent quantum system,
periodically perturbed by a rank one kick, acting on a separable
Hilbert space: $e^{iH_0T}e^{i\kappa T \phi \ket \bra
\phi}$ where $T$ and $\kappa$ are the period and the coupling
constant respectively. Assume the spectrum of the self adjoint
operator $H_0$ is pure point, simple, bounded
from below and the gaps between the eigenvalues $(\lambda_n)$ grow
like: $\lambda_{n+1}  \lambda_{n} \sim C n^d$ with $d \geq 2$. Under
some hypotheses on the arithmetical nature of the eigenvalues and on
the vector $\phi$, cyclic for $H_0$, we prove the Floquet
operator of the perturbed system has purely singular continuous spectrum.
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