On the repulsion of energy eigenstates in the time domain

The rate and extent of the exploration of the available phase space of a bound quantum mechanical system are shown to depend on the repulsion of energy eigenstates. Central to the argument is the Fourier transform relating the survival probability (in time) of an initially prepared nonstationary state and the (frequency) autocorrelation function of the excitation spectrum. Strong repulsion of states, as in the Wigner surmise, leads to a rapid dephasing of the initially coherently prepared state. The rate and extent of sampling of phase space depend not only on the spacing distribution but also on the intensity fluctuations. The rate of dephasing is equal to that inferred from the width of the spectral autocorrelation function.