Rate equations for quantum transport in multi-dot systems

Starting with the many-body Schr\"odinger equation we derive new rate equations for resonant transport in quantum dots linked by ballistic channels with high density of states. The charging and the Pauli exclusion principle effects were taken into account. It is shown that the current in such a system displays quantum coherence effects, even if the dots are away one from another. A comparative analysis of quantum coherence effects in coupled and separated dots is presented. The rate equations are extended for description of coherent and incoherent transport in arbitrary multi-dot systems. It is demonstrated that new rate equations constitute a generalization of the well-known optical Bloch equations.