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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• 0 citations
Publisher

Abstract

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/andp.199851007-811

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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.
The time of passage of the transmitted wave packet in a tunneling collision of a quantum particle with a square potential barrier becomes independent of the barrier width in a range of barrier thickness. This is the Hartman effect, which has been frequently associated with ``superluminality.'' A fundamental limitation on the effect is set by nonrelativistic ``causality conditions.'' We demonstrate first that the causality conditions impose more restrictive bounds on the negative time delays (time advancements) when no bound states are present. These restrictive bounds are in agreement with a naive, and generally false, causality argument based on the positivity of the ``extrapolated phase time,'' one of the quantities proposed to characterize the duration of the barrier's traversal. Nevertheless, square wells may in fact lead to much larger advancements than square barriers. We point out that close to the thresholds of new bound states, the time advancement increases considerably, while, at the same time, the transmission probability is large, which facilitates the possible observation of the enhanced time advancement.
Abstract The dynamics of absorption is analyzed by using an exactly solvable model that deals with an analytical solution to Schrödinger’s equation for cutoff initial plane waves incident on a complex absorbing potential. A dynamical absorption coefficient which allows us to explore the dynamical loss of particles from the transient to the stationary regime is derived. We find that the absorption process is characterized by the emission of a series of damped periodic pulses in time domain, associated with damped Rabi-type oscillations with a characteristic frequency, ω = ( E + ε )/ℏ, where E is the energy of the incident waves and − ε is energy of the quasidiscrete state of the system induced by the absorptive part of the Hamiltonian; the width γ of this resonance governs the amplitude of the pulses. The resemblance of the time-dependent absorption coefficient with a real decay process is discussed, in particular the transition from exponential to nonexponential regimes, a well-known feature of quantum decay. We have also analyzed the effect of the absorptive part of the potential on the dynamical delay time, which behaves differently from the one observed in attractive real delta potentials, exhibiting two regimes: time advance and time delay.