Differential conductance of a saddle-point constriction with a   time-modulated gate-voltage
  The effect of a time-modulated gate-voltage on the differential conductance $G$ of a saddle-point constriction is studied. The constriction is modeled by a symmetric saddle-point potential and the time-modulated gate-voltage is represented by a potential of the form $V_{0} \theta(a/2-|x-x_{c}|) \cos (\omega t)$. For $\hbar\omega$ less than half of the transverse subband energy level spacing, gate-voltage-assisted (suppressed) feature occurs when the chemical potential $\mu$ is less (greater) than but close to the threshold energy of a subband. As $\mu$ increases, $G$ is found to exhibit, alternatively, the assisted and the suppressed feature. For larger $\hbar\omega$, these two features may overlap with one another. Dip structures are found in the suppressed regime. Mini-steps are found in the assisted regime only when the gate-voltage covers region far enough away from the center of the constriction. 
C. S. Tang and C. S. Chu