  Coulomb coupled quantum dot arrays with staircase ground state configuration
have been proposed in literature for enhancing heat-harvesting and
refrigeration performance. However, due to their mutual Coulomb interaction, a
performance analysis of such systems remains complicated and necessitates
consideration of microscopic physics using density matrix formulation. However
the path of device analysis starting from the system Hamiltonian to density
matrix formulation is complicated and lacks the simplicity and intuitive aspect
of sequential electron transport conveyed by the quantum master equation (QME)
approach. In this paper, starting from the system Hamiltonian and employing the
density matrix formulation, I derive the QME of a system of three quantum dots,
two of which are electro-statically coupled. The framework formulated in this
paper can be further extended to derive QME of systems with higher number of
Coulomb coupled quantum dots.
