Non-Equilibrium Quantum Transport of Bosons through a Quantum Dot

The quantum dot coupled to reservoirs is known as a typical mesoscopic setup to manifest the quantum characteristics of particles in transport. In analogue to many efforts made on the study of electronic quantum dots in the past decades, we study the transport of bosons through such a device. We first generalize the formula which relates the current to the local properties of dot in the bosonic situation. Then, as an illustrative example, we calculate the local density of state and lesser Green function of the localized boson with a bosonic Fano--Anderson model. The current--voltage (I-V) behaviour at zero temperature is presented, and in the bosonic dot it is the I-V curve, in contrast to the differential conductance in the electronic dot, which is found to be proportional to the spectral function.