Abstract
The breaking of the generalized time-reversal symmetry of a quantum chaotic system corresponds to a transition from orthogonal to unitary ensembles of random matrices. Investigating this transition for the circular ensembles (applicable for time-dependent, periodic systems) the authors demonstrate and explain that there exists a relevant difference of the transition rate in comparison with the Gaussian ensembles appropriate for quantum conservative systems. The above supposition is supported by a numerical study of the eigenvalues and eigenvectors of the periodically kicked top.