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Annalen der Physik

Negative time delays in one dimensional absorptive collisions

Juan Gonzalo Muga, José P. Palao

Published Dec 1, 1998• 10 citations
Publisher

Abstract

Quantum scattering resonances are generally associated with a positive time delay. An example of anomalous negative time delay in resonance scattering is provided. The effect is due to an absorbing, negative imaginary part in the interaction potential.
DOI
10.1002/(sici)1521-3889(199812)7:7/8<671::aid-andp671>3.0.co;2-t

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The time delay or the time advance in the scattering of simple one-dimensional systems can be evaluated in a straightforward manner for certain potential models. It is found that when the interacting potential is attractive and has a strength such that it nearly supports an additional bound state, the time delay at small scattering energy is very large. On the other hand, if the potential supports a bound state with nearly zero binding energy, the time advance near threshold is anomalously large. The behavior of a wave packet scattering from the double delta-function potential is also investigated.
The time delay, as defined via phase shifts, does not apply to atom-atom collisions because of the semiclassical nature of the system. In this limit the contribution of one partial wave to the cross section is negligible. Therefore, we analyze time delay for the scattering amplitude and show that some new phenomena may occur, which cannot be explained by the time delay for a single phase shift. The time delay, which is averaged over all scattering angles, shows structure corresponding to several delay mechanisms. We also show that the lifetime of a resonance state, formed in a collision, may be considerably shorter than expected from the theory of resonance scattering.