Salecker–Wigner–Peres clock and average tunneling times

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).

Double General Point Interactions: Symmetry and Tunneling Times

“…It should also be noticed that apparent superluminality is more properly addressed in a relativistic theory. The above results on the GHE reinforce similar conclusions reached in Winful [1], Lunardi and Manzoni [20], Aharonov et al [21] and Lunardi et al [24]-an analysis of the GHE is, unavoidably, case-bycase and, thus, this work adds to the body of results clarifying such effect.…”

“…(31) The expression above for the clock (dwell) time agrees with previous results [21,23,24]. As previously mentioned, in this work we are particularly interested in the behavior of the tuneling times in the opaque regime (i.e., for |T| 2 ≪ 1 and |R| 2 ≃ 1).…”

“…p (k) → 0 in the extreme opaque limit |γ| → ∞, which is usually taken as an indication of the existence of the GHE [21,23,24]. However, Figure 1A shows that the off-resonance values of both the phase and clock (dwell) times clearly increase with the barrier separation-for the parameters in Figure 1A the scattering is well inside the opaque regimethus, contradicting the GHE, according to which one would expect the off-resonance times to be independent of the barrier spacing.…”

“…The vast literature discussing tunneling times and the HE, as well as its generalized version, focuses mostly in one-dimensional square potential barriers, with few other potentials such as the sech-square potential [22] and Dirac delta barriers (see, e.g., [21,23,24] and references therein) having been considered. From a practical point of view, the understanding of one-dimensional tunneling may help to understand phenomena in nanoscale systems such as, for example, conductance in nanowires (see [25] and references therein).…”

A Probability Distribution for Quantum Tunneling Times

“…The tunneling time scales considered in [23,28,31] involve taking an average over the spectral components of the transmitted wave packet and, thus, obscure the interpretation of the resulting average time. In this paper, we take as a starting point the real-valued average tunneling time obtained in [28], using the SWP quantum clock, and obtain a probability distribution of transmission times, by using a standard transformation between random variables. In addition to providing a more accurate time characterization of the tunneling process, this should provide a clearer connection with the experiments (which measure a distribution of tunneling times -see, e.g., Fig.…”