Time delay for an abstract quantum scattering process S Richard

Time delay for an abstract quantum scattering process S. Richard? Graduate School of Pure and Applied Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8571, Japan, E-mail: Dedicated to Prof. Hiroshi Isozaki on the occasion of this sixtieth anniversary Abstract In this short review paper, we discuss the concept of time delay for an abstract quantum scattering system. Its definition in terms of sojourn times is explained as well as its identity with the so-called Eisenbud-Wigner time delay. Necessary and natural conditions for such a construction 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. 1 Introduction Heuristically, the notion of time delay in scattering theory is quite easy to understand. Given a reference scattering process, this concept should indicate a measure of the advance or of the delay that a system acquires during a slightly different scattering process. In other words, the time delay should be a measure of an excess or a defect of time that a certain evolution process gets compared to an a priori process. The paradigm example of such two related systems consists in a classical particle evolving either freely in an Euclidean space or in the same Euclidean space but under the influence of a compactly supported potential.

• suitable triples


• quantum scattering


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• such


• time delay