Quantum transport, master equations, and exchange fluctuations

Abstract

We investigate to which extent a many-body Bloch-Redfield master-equation description of quantum transport is consistent with the exact generalized equilibrium conditions known as exchange fluctuation theorems. Thereby, we identify a class of master equations for which this is the case. Beyond this class, we find deviations which exhibit characteristic scaling laws as functions of the dot-lead tunneling, the interdot tunneling, and the temperature. These deviations are accompanied by an increase of lead energy fluctuations inherent in the Bloch-Redfield equation beyond a rotating-wave approximation. We illustrate our results with numerical data for a double quantum dot attached to four leads.