Statistical Approach to Tunneling Time in Attosecond Experiments

Tunneling, transport of particles through classically forbidden regions, is a pure quantum phenomenon. It governs numerous phenomena ranging from single-molecule electronics to donor-acceptor transition reactions. The main problem is the absence of a universal method to compute tunneling time. This problem has been attacked in various ways in the literature. Here, in the present work, we show that a statistical approach to the problem, motivated by the imaginary nature of time in the forbidden regions, lead to a novel tunneling time formula which is real and subluminal (in contrast to various known time definitions implying superluminal tunneling). This entropic tunneling time, as we call it, shows good agreement with the tunneling time measurements in laser-driven He ionization. Moreover, it sets an accurate range for long-range electron transfer reactions. The entropic tunneling time is general enough to extend to the photon and phonon tunneling phenomena.