Onset of chaos and its signature in the spectral autocorrelation function

The signature of chaos in the spectral autocorrelation function and in its Fourier transform, the survival probability, is shown to be in good agreement with the predictions of random matrix theory. An expression is proposed for the survival probability of an experimentally prepared nonstationary state when the dynamics are intermediate between chaotic and regular. Its validity is tested through the study of a model Hamiltonian . Two parameters can be extracted from the above observable, one which characterizes the level statistics and one which characterizes the distribution of transition intensities.