Semiclassics of rotation and torsion

Abstract

We discuss semiclassical approximations of the spectrum of the periodically kicked top, both by diagonalizing the semiclassically approximated Floquet matrix F and by employing periodic-orbit theory. In the regular case when F accounts only for a linear rotation periodic-orbit theory yields the exact spectrum. In the chaotic case the first method yields the quasienergies with an accuracy of better than 3% of the mean spacing. By working in the representation where the torsional part of the Floquet matrix is diagonal our semi-classical work is mostly an application of the asymptotics of the rotation matrix, i. e. of Wigner’s so-called d-functions.