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We report a study of spin dependent transport in a system composed of a quantum dot coupled to a normal metal lead and a ferromagnetic lead (NM-QD-FM). We use the master equation approach to calculate the spin-resolved currents in the presence of an external bias and an intra-dot Coulomb interaction. We find that for a range of positive external biases (current flow from the normal metal to the ferromagnet) the current polarization $\wp=(I_\uparrow-I_\downarrow)/(I_\uparrow+I_\downarrow)$ is suppressed to zero, while for the corresponding negative biases (current flow from the ferromagnet to the normal metal) $\wp$ attains a relative maximum value. The system thus operates as a rectifier for spin--current polarization. This effect follows from an interplay between Coulomb interaction and nonequilibrium spin accumulation in the dot. In the parameter range considered, we also show that the above results can be obtained via nonequilibrium Green functions within a Hartree-Fock type approximation.

We develop methods for calculating the zero-frequency noise for quantum shuttles, i.e. nanoelectromechanical devices where the mechanical motion is quantized. As a model system we consider a three-dot array, where the internal electronic coherence both complicates and enriches the physics. Two different formulations are presented: (i) quantum regression theorem, and (ii) the counting variable approach. It is demonstrated, both analytically and numerically, that the two formulations yield identical results, when the conditions of their respective applicability are fulfilled. We describe the results of extensive numerical calculations for current and current noise (Fano factor), based on a solution of a Markovian generalized master equation. The results for the current and noise are further analyzed in terms of Wigner functions, which help to distinguish different transport regimes (in particular, shuttling vs. cotunneling). In the case of weak inter-dot coupling, the electron transport proceeds via sequential tunneling between neighboring dots. A simple rate equation with the rates calculated analytically from the P(E)-theory is developed and shown to agree with the full numerics., 22 two-column pages, 9 figures

A small quantum dot coupled to two external leads is considered. Different signs of the dot-lead coupling matrix elements give rise to qualitatively different behavior of physical observables such as the conductance, the phase of the transmission amplitude, and the differential capacitance of the dot. For certain relative signs the conductance may vanish at values of the gate potential, where the spectral density is maximal. Zeroes of the conductance are robust against increasing the dot-lead coupling. They are associated with abrupt phase lapses in the transmission phase whose width vanishes as the square of the temperature. We carefully distinguish between phase lapses of $\ensuremath{-}\ensuremath{\pi}$ and phase antilapses of $\ensuremath{\pi}.$