# Multiple Fano Resonances in Dynamic Resonant Tunneling Processes
## 1 Introduction  
Tunneling and Resonant Tunneling are quantum processes that are extremely sensitive to a particle's energy. Consequently, when a system incorporates dynamic structures, its behavior can become much more complex. In general, perturbations, which are introduced into the system, usually tend to increase the tunneling current. This behavior manifests in activation [1, 2, 3, 4, 5, 6, 7, 8, 9] and the elevator effect [8, 9]. However, in some cases, for some specific energies, the tunneling current can be substantially suppressed [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]. In particular, it has been shown that 100% reflection occurs in certain cases. This conduct is related to Fano resonances [21, 22, 23, 24, 25, 26, 27, 28].  
Recently, a different presentation of current suppression and activation was demonstrated. It was shown that, when a particle penetrates an opaque barrier via a varying well, the process can be regarded as if the particle is trapped in a Quasi-Bound Super State (QBSS) [14], in a similar fashion to a Resonant Tunneling process, in which the particle is trapped in a Quasi-Bound State [29, 30, 31, 32]. The difference between these two scenarios is that the QBSS consists of multiple sub-quasi-states. Consequently, when an incoming particle's energy matches a high-amplitude spectral component of the QBSS, a high transmission occurs, and similarly, when no match occurs, the current is suppressed. It was noted that, at these energies, a destructive interference occurs in the well, which prevents particles from dwelling in this well, therefore preventing a high transmission. In these cases, the current decreases drastically; however, it is not necessarily reduced to zero, i.e., it does notnecessarily show Fano behavior. In fact, the same system may exhibit both behaviors for different energies in different cases.  
A Fano resonance occurs due to interference between a bound state and a continuum state. It is, therefore, not straightforwardly clear how a Fano resonance appears in a system that exhibits RT behavior. After all, an RT requires a quasi-bound state and not a bound one.  
The width of the barrier affects the resonance energy; however, in most research, this phenomenon has received little attention, mainly due to two reasons: first, in a resonant tunneling process, the barrier is usually opaque, and therefore its specific width has a negligible effect on the resonance energy (which predominantly depends on the shape of the potential well), and second, by narrowing the barrier, the resonance's spectral width increases (i.e., the particle's dwelling time in the well decreases); therefore, the resonance nature of the process fades away. Therefore, when the barrier is too narrow, it is fruitless to analyze the process as an RT one. This is indeed true in the stationary case, but in the dynamic case, the situation is much more complicated. Some of these effects have been observed in recent research [21; 27].  
We will show, in the following sections, that, by narrowing the barrier, not only does the resonance energy decrease drastically, but it can also be negative. Therefore, the barrier's width shrinkage can turn a resonance state into a bound one. Clearly, in a stationary scattering case, the bound state cannot be reached; however, in a dynamic case, the quasi-bound state generates a Fano resonance, which causes 100% reflection. Moreover, since the particle can lose/gain any number of energy quanta, then, if the oscillating frequency is low enough, by changing the barrier's width, multiple Fano resonances can occur for the same incoming particle's energy.