Semiclassical floquet spectra without periodic orbits from ħ-expansion of floquet matrix

Abstract

A full semiclassical quasienergy spectrum of the kicked top was recently calculated by diagonalizing the semiclassically approximated Floquet matrix. Classical orbits between prescribed initial and final points, real or of the ghost type, were incurred for the matrix elements rather than periodic orbits which arise in the Gutzwiller approach. In lowest order in ħ an accuracy of roughly 3% of the mean spacing was obtained for the quasienergies. We here extend the analysis to the next-to-leading order in ħ for the Floquet matrix. The accuracy for the quasienergy spectrum improves accordingly. Moreover, we thus explain why the previous leading-order treatment gave the mentioned 3% accuracy.