Quantum measurements and delays in scattering by zero-range potentials

TL;DR

This paper compares different quantum measurement approaches to determine the duration of scattering events, especially when the particle's wavelength is large, analyzing transmission, reflection, and elastic scattering.

Contribution

It applies quantum measurement theory to evaluate and compare the Eisenbud-Wigner-Smith delay and Larmor time in various scattering scenarios.

Findings

Eisenbud-Wigner-Smith delay and Larmor time differ significantly for large wavelengths.

Quantum measurement theory helps clarify which approach better estimates scattering duration.

Analysis covers transmission, reflection, and 3D elastic scattering cases.

Abstract

Eisenbud-Wigner-Smith delay and the Larmor time give different estimates for the duration of a quantum scattering event. The difference is most pronounced in the case where de-Broglie wavelength is large compared to the size of the scatterer. We use the methods of quantum measurement theory to analyse both approaches, and to decide which one of them, if any, describes the duration a particle spends in the region which contains the scattering potential. The cases of transmission, reflection and three-dimensional elastic scattering are discussed in some detail.