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Complexity measures and quantum revivals

E. Romera, F. de los Santos

Published May 3, 2010• 0 citations
OpenAlex

Abstract

We investigate a newly introduced generalized statistical complexity measure as applied to wave packet revival phenomena in the one-dimensional infinite square-well potential.

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We present an analytical investigation of revival phenomena in the finite square-well potential. The classical motion, revival, and super-revival time scales are derived exactly for wave packets excited in the finite well. These time scales exhibit a richer dependence on wave-packet energy and on potential-well depth than has been found in other quantum systems: They explain, for example, the difficulties in exciting wave packets with strong classical features at the bottom of a finite well, or with clearly resolved super-revivals in a shallow well. In the proper regions of validity, the time scales predict the instances of wave-packet reformation extremely accurately. Revivals at the bottom of the well are explored as a ``universal'' limit of the general theory, which offers the clearest connection with the series of fractional and full revivals seen in the dynamics of the infinite square-well potential.
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We have investigated quantum revivals of wave packets in a one-dimensional infinite square well potential containing a $\ensuremath{\delta}$ well in the middle. The time-dependent Schr\"odinger equation for this composite potential admits formally exact solutions. We present analytical results for revival properties in three physically motivated approximations: wave packets containing eigenstates with large numbers in the presence of an arbitrary $\ensuremath{\delta}$ well, ``shallow'' and ``deep'' $\ensuremath{\delta}$ wells. Analytical results in the case of a ``shallow'' $\ensuremath{\delta}$ well have been tested numerically.