The Exact Correspondence between Phase Times and Dwell Times in a Symmetrical Quantum Tunneling Configuration

TL;DR

This paper establishes an exact relationship between phase time and dwell time in symmetrical quantum tunneling, demonstrating that phase time accurately indicates particle positions and overcoming analytical challenges with wave packet decomposition.

Contribution

It provides the first explicit analytical connection between phase and dwell times in symmetrical quantum tunneling configurations, clarifying their physical interpretation.

Findings

Phase time accurately describes the position of scattered particles.

An exact relation between phase time and dwell time is derived.

Wave packet decomposition recovers precise particle positions.

Abstract

The general and explicit relation between the phase time and the dwell time for quantum tunneling or scattering is investigated. Considering a symmetrical collision of two identical wave packets with an one-dimensional barrier, here we demonstrate that these two distinct transit time definitions give connected results where, however, the phase time (group delay) accurately describes the exact position of the scattered particles. The analytical difficulties that arise when the stationary phase method is employed for obtaining phase (traversal) times are all overcome. Multiple wave packet decomposition allows us to recover the exact position of the reflected and transmitted waves in terms of the phase time, which, in addition to the exact relation between the phase time and the dwell time, leads to right interpretation for both of them.