Nature of the Quasi-Energy Spectrum of Quasi-Periodically Driven N -Level Quantum Systems

Extending recent work on two-level systems by Luck, Orland and Smilansky, we show that the Fourier transform of the time evolution operator of N -level systems, driven by a quasi-periodic external force generated from a Fibonacci sequence is not, in general, a denumerable set of δ-functions, implying that the dynamics is not quasi-periodic. The possibility of a mixed discrete and continuous spectrum for N ⩾ 3 is pointed out.