Phase times of electron passage through the self-similar fractal potential

Within the framework of the method developed previously for studying electron tunneling through the self-similar fractal potential (SFP), functional equations are derived for "phase tunneling times" (PTT). Their analysis shows that in the case of the SFP, the PTT cannot be interpreted as a dwell time of the particle in the barrier region. In particular, it turns out that the PTT through SFP barriers is negative for the short-wavelength region. This is also the case for SFP wells and electrons with arbitrary energy. It is shown that for the limiting SFP, when the fractal dimensionality is equal to unity, the PTT coincide with those for the δ-potential of the same power. Thus, the PTT are independent of the barrier width for the limiting SFP. This extraordinary result is caused by the fact that, as demonstrated previously, the probability that the electron with exactly preset energy is found inside the limiting SFP is equal to zero. ©2000 Plenum Publishing Corporation.