Effect of electron-phonon interaction in nanostructures and ultracold quantum gases

Abstract

The subject of this thesis is the effect of electron-phonon interaction in two classes of mesoscopic systems. The first class includes molecular quantum dots. They are believed to be good candidates for future realizations of transistors on the nanoscale. Using the concept of full counting statistics (FCS), the charge transfer for several models is characterized. On the one hand, the main focus of this work lies on systems with rather strong electron-phonon interactions, on the other hand, it lies on models with strongly correlated electrodes described by Tomonaga-Luttinger liquids. Based on a generalized Keldysh formalism, perturbative and non-perturbative methods have been provided to calculate the FCS. Using double quantum dot models, the analogy with multi-level systems is discussed. The second class contains the BEC polaron problem. The BEC polaron is based on the analogy of immersed quantum gases with electrons in crystal lattices. Using imaginary-time path integral Monte Carlo methods, variational principles and perturbation theory, the effective Frohlich model is investigated. The similarity to the emission of Cherenkov radiation is discussed.