Quantum Tunneling: The Longer the Path, the Less Time it Takes

The standard approaches to tunneling times are replaced by considering time correlation functions. A class of correlation functions that is always positive is identified and used to define quantum mechanical transition time probability distributions. The formalism is used to study the quantum dynamics of a thermal position correlation function of a parabolic barrier Hamiltonian. The transition time probability distribution between two points distributed symmetrically about the barrier top shifts to shorter times as the temperature is reduced and tunneling is increased. A study of the mean transition time as a function of the distance between the center of the initial and final densities shows that when the temperature is sufficiently low and tunneling dominates the dynamics, increasing the length of the path traversed decreases the mean transition time. The introduction of friction to the dynamics does not destroy this phenomenon, except when the friction coefficient is very large.