Fractional-order quantum kicked top map and its discrete dynamic behaviors

Abstract

A kind of top with a fractional operator is discussed in this paper. The top has a periodic nonlinear pulse kick sequence in the magnetic field and constant precessing around the magnetic field. Then, a fractional quantum kicked top map based on the Caputo derivative is proposed. The numerical solutions of the fractional difference equation are obtained, and the chaotic behavior is observed numerically in three aspects. Fractional quantum dynamics behaviors take place in a finite dimensional Hilbert space where the squared angular momentum is free precession. Finally, the dynamic behaviors of the fractional quantum kicked top map are systematically analyzed by using the bifurcation diagram, the phase diagram, and the maximum Lyapunov exponent.