Dynamic Resonant Tunneling
11. Summary
Resonant tunneling is a fascinating quantum phenomenon. In this chapter, we have focused on the transmission of a quantum particle through an opaque (mostly rectangular) barrier via a delta-function potential. We have discussed all dynamics regimes—stationary resonant tunneling, adiabatic changes, activation, forbidden activation, and instantaneous changes. The generic dynamic problem is highly complex. Each one of these regimes has its specific characteristics.
The main results are related to the domain in which the incoming particle’s energy is higher than the minimum eigenenergy of the changing well and the changes are fast enough to prevent particle escape. Unlike previous predictions, the fact that the particle can be trapped in the well does not mean by itself that it will necessarily be activated. In fact, in some cases,
the particle’s wavefunction experiences “destructive interference” inside the well, and as a consequence, activation is suppressed. We show that all the cases in which the potential’s temporal minima has a parabola shape have the same forbidden energies, and for the first time, we present a generic solution for this case.
Furthermore, the instantaneous case is also discussed for the first time. In this case, the dependence on the specific incoming energy vanishes, and a generic universal pattern appears.
Finally, we suggest testing this effect as a frequency effect transistor, which have the potential to be used as a highly accurate transistor.
Moreover, it is suggested that the effect of forbidden activation energies may explain the reason that humans can distinguish between 10,000 different odors while they have only several hundred odor receptors. According to this suggestion, every molecule can trigger different receptors, and only the combination of the activated ones creates the perception of the right smell. In any case, this research shows that dynamic resonant tunneling, in general (and forbidden activation, in particular), has a major, and totally nontrivial, role in the olfactory mechanism.
Author details
Er’el Granot* and Gilad Zangwill*
*Address all correspondence to: [email protected] and [email protected] Department of Electrical Electronics Engineering, Ariel University, Ariel, Israel
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the particle’s wavefunction experiences “destructive interference” inside the well, and as a consequence, activation is suppressed. We show that all the cases in which the potential’s temporal minima has a parabola shape have the same forbidden energies, and for the first time, we present a generic solution for this case.
Furthermore, the instantaneous case is also discussed for the first time. In this case, the dependence on the specific incoming energy vanishes, and a generic universal pattern appears.
Finally, we suggest testing this effect as a frequency effect transistor, which have the potential to be used as a highly accurate transistor.
Moreover, it is suggested that the effect of forbidden activation energies may explain the reason that humans can distinguish between 10,000 different odors while they have only several hundred odor receptors. According to this suggestion, every molecule can trigger different receptors, and only the combination of the activated ones creates the perception of the right smell. In any case, this research shows that dynamic resonant tunneling, in general (and forbidden activation, in particular), has a major, and totally nontrivial, role in the olfactory mechanism.
Author details
Er’el Granot* and Gilad Zangwill*
*Address all correspondence to: [email protected] and [email protected] Department of Electrical Electronics Engineering, Ariel University, Ariel, Israel
References
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