Coupled Nanomechanical Electron Shuttles: Full Stochastic Modeling and   Device-Level Simulation
  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. 
Mo Zhao and Robert H. Blick
quant-ph