D. Mugnai et al., KAC SOLUTION OF THE TELEGRAPHERS EQUATION FOR TUNNELING TIME ANALYSIS- AN APPLICATION OF THE WAVELET FORMALISM, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 50(2), 1994, pp. 790-797
A plausible description of traversal time was given, both in classical
ly allowed and forbidden regions, through a path-integral solution of
the telegrapher's equation. This analysis was applied to a simulation
based on microwave propagation in a waveguide considered as a one-dime
nsional system. An extension of the analysis has been performed in ord
er to compare the traversal (or delay) time results relative to a beat
-envelope signal with those as deduced from the distribution function
of the randomized time and its analytical continuation in imaginary ti
me. Subsequently, in tight analogy with a step signal in an electronic
circuit (zero-dimensional system), we have searched for a simulation
of traversal processes in real time, even for classically forbidden (t
unneling) processes. First we have considered a finite series expansio
n of harmonic functions of the signal in the neighborhood of its rise,
and applied the above mentioned procedure to each harmonic, implying
analytical continuation in imaginary time and an arbitrary truncation
in the range of the signal. Then, in order to avoid these shortcomings
, we have considered a waveletlike description of the signal.