Salecker-Wigner-Peres clock and average tunneling times

TL;DR

This paper employs the Salecker-Wigner-Peres quantum clock to analyze average tunneling times for wave packets scattering off static potentials, revealing that transmission times do not saturate in opaque barriers, challenging the Hartman effect.

Contribution

It introduces a method to compute average transmission and reflection times using a quantum clock with post-selection, applied to tunneling scenarios.

Findings

Average transmission time does not saturate for opaque barriers.

No evidence of the Hartman effect in the studied regimes.

Behavior analyzed for Gaussian wave packets on rectangular and double delta barriers.

Abstract

The quantum clock of Salecker-Wigner-Peres is used, by performing a post-selection of the final state, to obtain average transmission and reflection times associated to the scattering of localized wave packets by static potentials in one dimension. The behavior of these average times is studied for a gaussian wave packet, centered around a tunneling wave number, incident on a rectangular barrier and, in particular, on a double delta barrier potential. The regime of opaque barriers is investigated and the results show that the average transmission time does not saturate, showing no evidence of the Hartman effect (or its generalized version).