Quantum Shuttle: Physics of a Numerical Challenge.

Shuttle devices are a class of nanoelectromechanical systems generically described as movable single electron transistors. They exhibit an electromechanical instability from the standard tunnelling regime to the shuttling regime in which the quantum dot oscillates and transfer one electron per cycle. I present a theory for the device in which both the electrical and mechanical degrees of freedom are quantized. The different operating regimes are detected by analyzing current, noise and Wigner function distributions. The calculation of the stationary solution for the Generalized Master Equation which describes the system dynamics is the starting point for the evaluation of these quantities and represents a numerically challenging problem due to the size of the Hilbert space necessary to capture the tunnelling to shuttling transition. [ABSTRACT FROM AUTHOR]