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We show that regular and irregular spectral statistics have direct, distinctive, and observable time-dependent manifestations in the behavior of the survival probability P(t)={}〈{ψ}(0){}{ψ}(t)〉², averaged over Hamiltonian ensembles and initial conditions. Specifically, systems exhibiting energy-level repulsion display characteristically strong decorrelations at short times. The proof relies solely on Liouville spectral properties of ensembles of bound quantum systems.
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Wilkie et al. (1991) studied this question.
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