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Spectral properties of a periodically kicked quantum Hamiltonian. (English) Zbl 0713.58044
Summary: We study the spectral properties of the Floquet operator for the periodically kicked Hamiltonian \(H(t)=H_ 0+\lambda \phi ><\phi \sum^{-\infty}_{+\infty}\delta (t-nT),\) \(H_ 0\) being self-adjoint and pure point (for the meaning of \(<>\) in this formula see the paper itself). We show that the Floquet operator is pure point for almost every \(\lambda\), if \(\phi\) is cyclic for \(H_ 0\) and has absolutely convergent expansion in the basis of eigenstates of \(H_ 0\). When this last condition is not satisfied, the Floquet operator can have a continuous spectrum, as we show by an example.

MSC:
37A30 Ergodic theorems, spectral theory, Markov operators
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
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