  Earlier theory and measurements show that nanomechanical electron shuttles
can work as ratchets for radio-frequency rectification, but its performance was
hard to predict so far. This paper focuses on the coupled shuttles which can
potentially break symmetry better than a single shuttle. We propose a full
stochastic model of coupled shuttles, where the mechanical motion of
nanopillars and the incoherent electronic tunneling are modeled as a Markov
chain. A linear master equation is constructed. In particular, the interaction
of the their randomness is taken into account. This model favors analyzing the
symmetry breaking that results in the observed rectification
current~\cite{Kim2010_PRL}. Further, based on the model we propose the
deterministic equations of mean physical variables by assuming multivariate
Gaussian distribution, which enables complex device simulation and design.

Quantum Physics