Electronic states and vibrons in carbon nanotube quantum dots have in general different location and size. As a consequence, the conventional Anderson-Holstein model, coupling vibrons to the dot total charge only, may no longer be appropriated in gen
eral. Here we explicitly address the role of the spatial fluctuations of the electronic density, yielding space-dependent Franck-Condon factors. We discuss the consequent marked effects on transport which are compatible with recent measurements. This picture can be relevant for tunneling experiments in generic nano-electromechanical systems.
We study non-adiabatic two-parameter charge and spin pumping through a single-level quantum dot with Coulomb interaction. For the limit of weak tunnel coupling and in the regime of pumping frequencies up to the tunneling rates, $Omega lesssim Gamma/h
bar$, we perform an exact resummation of contributions of all orders in the pumping frequency. As striking non-adiabatic signatures, we find frequency-dependent phase shifts in the charge and spin currents, which allow for an effective single-parameter pumping as well as pure spin without charge currents.
Population of a phononic mode coupled to a single-electron transistor in the sequential tunneling regime is discussed for the experimentally realistic case of intermediate electron-phonon coupling. Features like a sub-Poissonian bosonic distribution
are found in regimes where electron transport drives the oscillator strongly out of equilibrium with only few phonon states selectively populated. The electron Fano factor is compared to fluctuations in the phonon distribution, showing that all possible combinations of sub- and super-Poissonian character can be realized.
