Exact Steady-state Solution of Electron Transport Through a Quantum System Coupled with Dissipative Electrodes

In the framework of the Lindblad quantum master equation, we develop a theory which allows us to describe electron transport through a molecular junction coupled with dissipative electrodes. We generalize the theory of coherent quantum transport and include the electronic dissipation in electrodes. Moreover, we derive an exact solution of steady-state current and analyze the asymptotic behavior in the different limits of electronic dissipation. Furthermore, we obtain a Landauer-type formula and show that this formula can be reduced to the original Landauer formula in the condition of zero dissipation rate.