On quantum twist maps and spectral properties of Floquet operators

Quantum twist maps an introduced as the representatives of "kicked" quantum systems in the Heisenberg picture and their orbit structures are related to the various spectral types of the corresponding Floquet operators U-V(T, 0). By means of geometrical RAGE methods a la Enss and Veselic sufficient conditions for the absence of sigma(ac)(U-V (T, 0)), respectively sigma(cont)(U-V(T, 0)) are derived, For the example of h(t) = -id/d theta + V (theta).Sigma(j) delta (t -jT), defined on L-1(S-1, d theta), the quasi-energy spectrum sigma(U-V (T, 0)) as well as the orbit structure of the twist map are determined for all V is an element of C-3 (S-1) in case of T/2 pi is an element of Q, respectively for T/2 pi an irrational number of constant type. (C) Elsevier, Paris.