Time Delay of Quantum Scattering Processes

R. G. Tee

Abhisek Mohapatra, Kalyan B. Sinha, W. O. Amerin

The time-delay in a simple quantum mechanical scattering process is a simple mechanical scattering process is defined to be the limit as r→∞ of the difference of the sojourn times of a scattering state and of the associated free state in a ball of radius r, with the particle under the influence of a potential W(x). For W(x) ~ |x| −α (α>1) at infinity, we use a smooth localization function with the tail growing like r 1−α (δ>0, depending on W) instead of the characteristic function of a ball of radius r and it is shown that the time-delay exists and satisfies the Eisenbud-Wigner relation.

Serge Richard

In this short review paper, we discuss the concept of time delay for an abstract quantum scattering system.Its definition in terms of sojoum times is explained as well as its identity with the so-called Eisenbud-Wigner time delay.Necessary and natural conditions for such a constmction are introduced and thoroughly discussed.Assumptions and statements are pre- cisely formulated but proofs are contained in two companion papers written in collaboration with R. Tiedra de Aldecoa.

Jingbo Wang

Christian Gérard, Rafael Tiedra de Aldecoa

We advocate for the systematic use of a symmetrized definition of time delay in scattering theory. In two-body scattering processes, we show that the symmetrized time delay exists for arbitrary dilated spatial regions symmetric with respect to the origin. It is equal to the usual time delay plus a new contribution, which vanishes in the case of spherical spatial regions. We also prove that the symmetrized time delay is invariant under an appropriate mapping of time reversal. These results are also discussed in the context of classical scattering theory.

Arne Jensen