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

TL;DR

This paper investigates charge conservation violations in a quantum dot system using generalized master equations, revealing discrepancies between different calculation methods due to multiple baths, which challenges foundational assumptions in open quantum system theory.

Contribution

It demonstrates that simultaneous coupling to electronic leads and a dissipative bath can cause unphysical results in current noise calculations, highlighting a fundamental issue in modeling open quantum systems.

Findings

Current noise between dots can be negative, indicating charge conservation breaking.

Counting variable approach yields physically plausible noise results.

Discrepancy arises from the presence of multiple baths in the system.

Abstract

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 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. 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, 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.