The tunnelling current through oscillating resonance and the sisyphus effect

The tunnelling current through an oscillating resonance level is thoroughly investigated exactly numerically and with several approximations - analytically. It is shown that while the oscillations can increase the tunnelling current (and in several cases the increase is exponentially large), their main effect is to reduce it dramatically at certain energies. In fact, the current in the presence of the oscillations cannot increase the maximum current of the adiabatic solution. That is why, while the elevator effect does occur in this system, the Sisyphus effect is the more dominant and prominent one.