We study the dynamics of a quantum rotator, impulsively kicked according to the almost-periodic Fibonacci sequence. A special numerical technique allows us to carry on this investigation for as many as ${10}^{12}$ kicks. It is shown that above a critical kick strength, the excitation of the system is well described by regular diffusion, while below this border it becomes anomalous and subdiffusive. A law for the dependence of the exponent of anomalous subdiffusion on the kick strength is established numerically. The analogy between these results and quantum diffusion in models of quasicrystals and in the kicked Harper system is discussed.

• Received 27 July 2000

DOI:https://doi.org/10.1103/PhysRevE.63.066217