Time-delay of classical and quantum scattering processes: a conceptual overview and a general definition

TL;DR

This paper offers a comprehensive conceptual overview and a unified definition of time-delay in classical and quantum scattering, clarifying foundational issues and proposing a new interpretation of sojourn and delay times.

Contribution

It introduces the concepts of fuzzy and free-flight sojourn times to define quantum time-delay in a general, multichannel scattering context, with a novel interpretative perspective.

Findings

Unified definition of quantum time-delay for various scattering systems

Clarification of the conceptual foundations of sojourn and delay times

Proposal of a new interpretation of quantum sojourn and delay times

Abstract

We present a step by step introduction to the notion of time-delay in classical and quantum mechanics, with the aim of clarifying its foundation at a conceptual level. In doing so, we motivate the introduction of the concepts of "fuzzy" and "free-flight" sojourn times, that we use to provide the most general possible definition for the quantum time-delay, valid for simple and multichannel scattering systems, with or without conditions on the observation of the scattering particle, and for incoming wave packets whose energy can be smeared out or sharply peaked (fixed energy). We conclude our conceptual analysis by presenting what we think is the right interpretation of the concepts of sojourn and delay times in quantum mechanics, explaining why, in ultimate analysis, they shouldn't be called "times".