A quantum Markovian master equation is derived to describe the current noise in resonant tunnelling devices. This equation includes both incoherent and coherent quantum tunnelling processes. We show how to obtain the population master equation by adiabatic elimination of quantum coherences in the presence of elastic scattering. We calculate the noise spectrum for a double well device and predict sub-shot noise statistics for strong tunnelling between the wells. The method is an alternative to Greenu27s functions methods, and population master equations for very small coherently coupled quantum dots.
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