1212.6506 (Charis Anastopoulos et al.)

Quantum temporal probabilities in tunneling systems: I. Tunneling times
in quantum field theory    [PDF]

Charis Anastopoulos, Ntina Savvidou

We study the temporal aspects of quantum tunneling as manifested in time-of-arrival experiments, in which the detected particle tunnels through a potential barrier. In particular, we present a general method for constructing temporal probabilities in tunneling systems that (i) defines `classical' time observables for quantum systems and (ii) applies to relativistic particles interacting through quantum fields. We show that the relevant probabilities are defined in terms of specific correlations functions of the quantum field associated to tunneling particles. We construct a probability distribution with respect to the time of particle detection that contains all information about the temporal aspects of the tunneling process. In specific cases, this probability distribution leads to the definition of a delay time that, for parity-symmetric potentials, reduces to the phase time of Bohm and Wigner. We apply our results to piecewise constant potentials, by deriving the appropriate junction conditions on the points of discontinuity. For the double square potential, in particular, we demonstrate the existence of (at least) two physically relevant time parameters, the delay time and a decay rate that describes the escape of particles trapped in the inter-barrier region.

View original: http://arxiv.org/abs/1212.6506