We consider the possibility of parametric amplification of a mechanical vibration mode of a nanowire due to its interaction with a Bose-Einstein condensate (BEC) of ultracold atoms. The magneto-mechanical coupling is mediated by the vibrationally mod
ulated magnetic field around the current-carrying nanowire, which can induce atomic transitions between different hyperfine sublevels. We theoretically analyze the limitations arising from the fact that the spin inverted atomic medium which feeds the mechanical oscillation has a finite bandwidth in the range of the chemical potential of the condensate.
We propose a definition for the Polya number of continuous-time quantum walks to characterize their recurrence properties. The definition involves a series of measurements on the system, each carried out on a different member from an ensemble in orde
r to minimize the disturbance caused by it. We examine various graphs, including the ring, the line, higher dimensional integer lattices and a number of other graphs and calculate their Polya number. For the timing of the measurements a Poisson process as well as regular timing are discussed. We find that the speed of decay for the probability at the origin is the key for recurrence.
