Tunnelling times and the "hartman effect"

Olkhovsky, Vladislav S. and Recami, Erasmo and Zaichenko, Aleksandr K. (1995) Tunnelling times and the "hartman effect". Accademia Peloritana dei Pericolanti, Classe di Scienze FF. MM. NN., LXXIII. pp. 199-225.

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atti_3_1995_199.pdf - Submitted Version

In a recent review paper [Phys. Rpeorts 214 (1992) 339] we proposed, within conventional quantum mechanics, new definitions fot the subarrier tunnelling and reflection times. Aims of the present paper are: (i) presenting and analysing the results of various numerical calculations (based on our equations) on the penetration and return times $\left \langle tau_P_e_n \right \rangle$ , $\left \langle tau_R_e_t\right \rangle$ during tunnelling inside a rectangular potential barrier, for various penetration depths $x_f$ ; (ii) putting forth and discussing suitable definitions. Besides of the mean values, also of the variances (or dispersions)$D\tau_T\$ and $D\tau_R\$ for the tima durations of trasmission and reflection processes; (iii) mentioning that our definition $\left \langle tau_T \right \rangle$ for the average transmission time results to constituite an improvemente of the ordinary dwell-time $\bar tau^D^W\$ formula: (iv) commenting upon some recent criticism by C.R. Leavens, on the basis of our new numerical results. We stress that our numerical evaluations confirm that our approach implied, and implies, the existence of the Hartman effect: an effect that in these days (due to the theoretical connections between tunnelling and evanescent-wave propagation) is receiving - at Cologne, Berkeley, Florence and Wien - indirect, but quite interesting, experimental verifications. At last we briefly analyze some other definitions of tunnelling times.