Decoherent histories approach to tunneling times and its implication

Decoherent histories approach to quantum mechanics assigns probabilities to events that are not restricted to a single moment of time, provided that the decoherence condition holds for the set of events. The condition is however hardly satisfied in general, which has been considered to limit the usefulness of the histories approach. The present paper applies the histories approach to the tunneling time problem to show that, although the decoherence condition does not hold, the histories approach is still useful in predicting the central tendency and the dispersion of resident times. We consider such quantities that would become the average and the standard deviation of resident times if the decoherence condition held. Since the condition does not actually hold, they are not regarded as the true average and the true standard deviation. Nevertheless, a quantum clock approach allows us to interpret these quantities as a central value and a dispersion of resident times within the time resolution of the clock