Master equations are an increasingly popular framework for the simulation of (time--dependent) electronic transport in nanoscale devices. Most of these approaches take the the Markovian limit for relaxation of charge carriers and thus are phenomenological in nature. Starting from a Lindblad equation, we derive the relationship between widely adopted master equations and determine where they yield physically meaningful results. As long as extended reservoirs -- explicit degrees of freedom associated with the electrodes -- are present, the applicability of the Lindblad equation does not require a large bias or even ``true Markovianity.'' While the Lindblad equation is completely positive and respects Pauli exclusion for any relaxation strength, physically meaningful results require that this relaxation be weaker than its thermal counterpart and that extended reservoirs are ``large enough'' in a sense that we quantify. In addition to presenting the exact, closed form solution to the Lindblad equation for interacting and noninteracting systems alike, our results clarify the use and domain of applicability of Markovian master equations for quantum transport.
Citation: The Journal of Chemical Physics
Pub Type: Journals