Charge conservation breaking within a generalized master equation description of electronic transport through dissipative double quantum dots

We report an observation of charge conservation breaking in a model study of electronic current noise of transport through a dissipative double quantum dot within a generalized master equation formalism. We study the current noise through a double quantum dot coupled to two electronic leads in the high bias limit and a dissipative heat bath in the weak coupling limit. Our calculations are based on the solution of a Markovian generalized master equation. The zero-frequency component of the current noise calculated within the system, i.e., between the two dots, via the quantum regression theorem exhibits unphysical negative values. On the other hand, the current noise calculated for currents between the dots and the leads by the counting variable approach shows no anomalies and seems physically plausible. We inquire into the origin of this discrepancy between two nominally equivalent approaches and show that it stems from the simultaneous presence of the two types of baths, i.e., the electronic leads and the dissipative bosonic bath. This finding raises interesting questions concerning conceptual foundations of the theory describing multiple-baths open quantum systems widely encountered in nanoscience.