Time delay for an abstract quantum scattering process

TL;DR

This paper reviews the concept of time delay in abstract quantum scattering systems, explaining its definition via sojourn times and its relation to Eisenbud-Wigner time delay, with detailed conditions and mathematical formulation.

Contribution

It provides a comprehensive discussion of the theoretical framework and conditions for defining time delay in abstract quantum scattering, including precise assumptions and formulations.

Findings

Clarifies the definition of time delay via sojourn times

Establishes the identity with Eisenbud-Wigner time delay

Discusses necessary conditions for the construction

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 precisely formulated but proofs are contained in two companion papers written in collaboration with R. Tiedra de Aldecoa.