Communication: Master equations for electron transport: The limits of the Markovian limit
Justin E. Elenewski, Daniel S. Gruss, Michael P. Zwolak
Master nist-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 nist-equation, we derive the relationship between widely adopted master nist-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 nist-equation does not require a large bias or even ``true Markovianity.'' While the Lindblad nist-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 nist-equation for interacting and noninteracting systems alike, our results clarify the use and domain of applicability of Markovian master nist-equations for quantum transport.