Emergence of Chaos in nano-electromechanical shuttles with hard-wall collision: Nonanalytic charge transport

We develop a theory for charge transport in nano-electromechanical shuttles in the presence of hard-wall collision. We show that, in certain regimes, the time-averaged charge current is not predictable and is not an analytic function of applied voltage. The rectified electric current and its non-analyticity emerge from a non-Markovian process in the presence of the hard-wall collision, which causes chaotic motion of the shuttle.