Barrier resonance

Figure 3.1 A schematic diagram showing the relationship of reactive resonances to the vibrationally adiabatic potential curve. The upper panel illustrates a Feshbach resonance trapped in a well the lower panel shows a barrier resonance or QBS.

A second scenario is provided by barrier-type resonances (sometimes referred to as quantum bottleneck states [QBS]), which do not rely on the internal excitation of the collision complex for their existence. In fact, barrier resonances are observed even when there is no well in Vad(s n). Collisional time delay occurs near the barrier maximum simply because the motion along the s-coordinate slows down passing over the barrier, as in the lower... 

Feshbach resonances is purely model dependent since trapping well may exist on one type of adiabatic potential, say in hyperspherical coordinates, while only a barrier may exist on another type, say in natural collision coordinates. However, this is not correct since there are fundamental differences between QBS and Feshbach states. First, the pole structure of the S-matrix is intrinsically different in the two cases. A Feshbach resonance corresponds to a single isolated pole of the scattering matrix (S-matrix) below the real axis of the complex energy plane, see the discussion below. On the other hand, the barrier resonance corresponds to an infinite sequence of poles extending into the lower half plane. For a parabolic barrier, it is easy to show that the pole positions are given by... 

One expects to observe a barrier resonance associated with each vibra-tionally adiabatic barrier for a given chemical reaction. Since the adiabatic theory of reactions is closely related to the rate of reaction, it is perhaps not surprising that Truhlar and coworkers [44, 55] have demonstrated that the cumulative reaction probability, NR(E), shows the influence barrier resonances. Specifically, dNR/dE shows peaks at each resonance energy and Nr(E) itself shows a staircase structure with a unit step at each QBS energy. It is a more unexpected result that the properties of the QBS seem to also imprint on other reaction observables such as the state-to-state cross sections [1,56] and even can even influence the helicity states of the products [57-59]. This more general influence of the QBS on scattering observables makes possible the direct verification of the existence of barrier-states based on molecular beam experiments. 

For both the Feshbach resonance in F+HD and the barrier resonance in H+HD, the trapped resonance state was localized close to the saddle point. Thus, the complexes correspond to the intermediates with partially formed (or broken) bonds. The F+HCl-tHF+Cl reaction illustrates a third category of resonance, the prereactive (and postreactive) resonance. In this case, the bonding of the reagent (or product) is only weakly perturbed by the colliding... 

R.S. Freidman, D.G. Truhlar, Barrier resonances and chemical reactivity, in D.G. Truhlar, B. Simon, (Eds.), Multiparticle Quantum Scattering with Applications to Nuclear, Atomic, and Molecular Physics, Springer-Verlag, New York, 1997, p. 243. 

THE EQUIVALENT CIRCUIT OF SPIN-DEPENDANT TRANSPORT IN DOUBLE-BARRIER RESONANT TUNNELING... 

Localization of energy exchanges in field-assisted double-barrier resonant tunneling... 

Localization of Energy Exchanges in Field-Assisted Double-Barrier Resonant Tunneling 181... 

E. Scholl, A. Amann, M. Rudolf, and J. Unkelbach Transverse spatio-temporal instabilities in the double barrier resonant tunneling diode, Phys-ica B 314, 113 (2002). 

Figure 7.3 Distribution of the first 15 complex poles in the fourth quadrant of the k plane of the quadruple barrier resonant tunneling system with parameters given in the text.

As another example, we consider a double-barrier resonant tunneling system in ID. These artificial quantum systems, formed of semiconductor materials, have been fabricated and studied since the 1970s of last century [61]. Sakaki and co-workers verified experimentally that electrons in sufficiently thin symmetric double-barrier resonant structures exhibit exponential decay [88]. Recent work has examined the conditions for full nonexponential decay in double-barrier resonant systems [56]. Here we want to exemplify the time evolution of the probability density in these systems along the external region using the resonant expansion given by Eq. (121) [89]. 

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