Nano-devices are electronic components of mesoscopic scale, whose small dimensions allow the study of fundamental issues concerning the quantum coherence of the electrons and the nature of their interactions. The focus of this talk will be on the connection between two problems that are of interest within this realm and that at first sight might seem quite different: an electron that tunnels through a region where it can interact with a phonon mode (problem (a)) and the one where the scattering region is subject to a time-periodic Hamiltonian (problem (b)). In the first part of this talk I will briefly present a quantum coherent framework for the solution of problem (a). The method is variational (non perturbative) in the electron-phonon coupling strength and has been used to solve a variety of transport problems in semiconductor and molecular devices. In the second part of the talk, I will show how problem (b) can be solved in a similar way through the use of Floquet theory.