Effects of incoherent processes on the quantum transport through a finite-range time-modulated potential

We study the effect of phase randomization on the quantum transport through a finite-range time-modulated potential. The time-modulated potential lead s only to coherent inelastic scatterings, and the incoherent processes are described by an S-matrix model proposed originally by Buttiker for the case of time-independent transport. This S-matrix model provides us a systemati c way to reinject into the system those electrons that have suffered with i ncoherent scatterings. The distribution of these reinjected electrons is de termined by an effective chemical potential <(<mu>)over tilde>. For compari son, we study the cases where the incoherent processes occur inside and out side the time-modulated region. The incoherent processes are found to broad en and to smear the structures in the conductance G that are associated wit h the coherent inelastic scatterings. However, the smearing is more effecti ve when the incoherent processes occur inside the time-modulated potential region.