Effect of symmetry breaking on ‘‘chaotic’’ eigenfunctions

The theory of random matrices predicts that the eigenvector statistics of quantum operators associated with chaotic dynamics should undergo a rapid transition from one universality class to another as a symmetry of the system is gradually broken. We show by a numerical calculation that the transition in strength correlations of the eigenvector components are identicial to the random-matrix predictions for time-reversal violations. This transition turns out to be governed by the same parametrization as in the case of spectral fluctuations of these systems but the speed of transition is different for the two cases. © 1996 The American Physical Society.