In this project we will develop a formalism based on the non-equilibrium Green functions for the perturbative description of various inelastic electron tunneling spectroscopy (IETS) features such as formulation in terms of scattering states, IETS for molecules with negative interference including the overtones signal, and consistent description of the IETS line-width. Furthermore, we will use the path-integral Monte Carlo and recently developed memory function formalism for the numerical calculation of structural as well as transport properties of non-equilibrium versions of Anderson-Holstein and Peierls instability models.

We will develop a nonequilibrium-Green-functions-based description of various features of inelastic electron tunneling spectroscopy in nanosystems with negative interference. We will also address via Quantum Monte Carlo nonperturbative structural effects in nonequilibrium electron-vibration models.