Average quantum tunneling times for asymmetric potentials

We generalize a recent definition of average quantum tunneling times, using the Salecker-Wigner-Peres (SWP) clock, to be applicable to the tunneling of a localized wave packet through asymmetric potentials. We investigate the properties of the average transmission and reflection times, including their interpretation in the framework of the weak measurement theory, and compare them with other standard average times. Finally, we discuss the advantages of the definition of average tunneling times as prescribed by the SWP clock (such as the non-saturation of the transmission time for opaque barriers).