  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 Green's functions methods, and population
master equations for very small coherently coupled quantum dots.
