Self-similar spectrum in effective time independent Hamiltonians for kicked systems

Abstract

We study multifractal properties in the spectrum of effective time-independent Hamiltonians obtained using a perturbative method for a class of delta-kicked systems. The evolution operator in the time-dependent problem is factorized into an initial kick, an evolution dictated by a time-independent Hamiltonian, and a final kick. We have used the double kicked SU(2) system and the kicked Harper model to study butterfly spectrum in the corresponding effective Hamiltonians. We have obtained a generic class of SU(2) Hamiltonians showing self-similar spectrum. The statistics of the generalized fractal dimension is studied for a quantitative characterization of the spectra.