A SIMPLE KINETIC-EQUATION FOR STEADY-STATE QUANTUM TRANSPORT

An important problem in quantum transport is to understand the role of dissipative processes. In this paper the author assume a model in which phase-breaking and dissipation are caused by the interaction of electrons with a reservoir of oscillators through a delta potential. In this model the self-energy is a delta function in space, leading to a kinetic equation with a simple physical interpretation. A novel treatment of the contacts is used to introduce the external current into the kinetic equation. One specializing to linear response the author obtains an integral equation that looks like the Buttiker formula (1961) extended to a continuous distribution of probes. The author show that this equation can be reduced to the usual Buttiker formula which involves only the actual physical probes. Dissipation modifies the transmission coefficients, and the author presents explicit expressions derived from this model. Also, in a homogeneous medium the integral equation reduces to the diffusion equation, it the electrochemical potential is assumed to vary slowly. This paper serves to establish a bridge between the quantum kinetic approach which rigorously accounts for the exclusion principle and the one-particle approach which is intuitively appealing.