Chapter 4: Classical-Quantum Correspondence

Within the general context of classical-quantum correspondence falls the interesting topic of fractional revivals of wavepackets. Ehrenfest's theorem tells us that on sufficiently short, time scales, the quant um expectation values The Actual Formul evolve in the same way as do the classical variables The Actual Formul However, on longer timescales for anharmonic potentials Ehrenfest's theorem quite generally breaks down. It is a remarkable fact that on a still much longer time scale there is, in many cases of interest., an almost complete revival of t he wavepacket, and a second Ehrenfest epoch. In between these full revivals are an infinite number of fractional revivals which collectively have an interesting mathematical structure. The concept of an Ehrenfest time applies again to each of these fractional revivals.
I. Sh. Averbukh and N.F. Perelman, The dynamics of wave packets of highly-excited states of atoms and molecules, Sov. Phys. Usp. 34, 572 (1991).