We discuss methods for numerically solving the generalized Master equation GME which governs the time-evolution of the reduced density matrix of a mechanically movable mesoscopic device in a dissipative environment. As a specific example, we consider the quantum shuttle -- a generic quantum nanoelectromechanical system (NEMS). When expressed in the oscillator basis, the static limit of the GME becomes a large linear non-sparse matrix problem (characteristic size larger than 10^4 by 10^4) which however, as we show, can be treated using the Arnoldi iteration scheme. The numerical results are interpreted with the help of Wigner functions, and we compute the current and the noise in a few representative cases.
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