Kramers' Degeneracy and Quartic Level Repulsion

An elementary technique, based on almost degenerate perturbation theory, is used to establish the association between (unitary and antiunitary) symmetries and universality classes of level repulsion for autonomous and periodically driven quantum systems. For one such class, characterized by Kramers' degeneracy and quartic level repulsion, we present a simple example, a periodically kicked top with half-integer angular momentum, which has one antiunitary symmetry (a generalized time reversal) but no unitary symmetry; in the classical limit that top behaves chaotically.