  Soft nanosystems are electronic nanodevices, such as suspended carbon
nanotubes or molecular junctions, whose transport properties are modulated by
soft internal degrees of freedom, for example slow vibrational modes. In this
review, effects of the electron-vibration coupling on the charge and heat
transport of soft nanoscopic systems are theoretically investigated in the
presence of time-dependent perturbations, such as a forcing antenna or pumping
terms between the leads and the nanosystem. A well established approach valid
for non-equilibrium adiabatic regimes is generalized to the case where external
time-dependent perturbations are present. Then, a number of relevant
applications of the method are reviewed for systems composed by a quantum dot
(or molecule) described by a single electronic level coupled to a vibrational
mode. Before introducing time-dependent perturbations, the range of validity of
the adiabatic approach is discussed showing that a very good agreement with the
results of an exact quantum calculation is obtained in the limit of low level
occupation. Aim of this review has been to discuss common features of different
soft nanosystems under external drive. The most interesting effects induced by
time-dependent perturbations are obtained when the external forcing is nearly
resonant with the slow vibrational modes. Indeed, not only the external forcing
can enhance the electronic response, but it also induces nonlinear regimes
where the interplay between electronic and vibrational degrees of freedom plays
a major role.
