Open orbits and the semiclassical dwell time

TL;DR

This paper presents a semiclassical approach to calculating the Wigner delay time in chaotic scattering using open orbits, highlighting its strengths and limitations in assessing time delay moments and fluctuations.

Contribution

It introduces a classical-path-based semiclassical expression for the energy-averaged Wigner time delay and discusses its limitations in higher moments estimation.

Findings

Semiclassical expression for average Wigner time delay derived

Method effectively captures classical paths in chaotic scattering

Limitations identified in semiclassical estimation of higher moments

Abstract

The Wigner delay time is addressed semiclassically using the Miller's S-matrix expressed in terms of open orbits. This leads to a very appealing expression, in terms of classical paths, for the energy averaged Wigner time delay in chaotic scattering. The same approach also puts in evidence the semiclassical incapability to correctly assess the time delay higher moments. This limitation suggests that the use of the semiclassical approximation to quantify fluctuations in scattering phenomena, like in mesoscopic physics, has to be considered with great caution.