Quantum Dissipation at the Nanoscale

The outline of this work will be as follows: in chapter 1, after a brief overview of the systems studied and a preview of the results obtained, we will introduce the general models and methods we are going to use to tackle the systems considered, hopefully providing enough theory to understand our later extensive treatment, without entering in too much detail in the widely studied general theories of our models. In chapter 2 we will show our first application: the description of a spin-sensitive dissipation channel compatible with the experimental findings of an atomic force microscopy experiment. We will describe in some detail the experiment and the system under study and why some direct approaches are unable to account for the observed effect; we will then specialize the previously described path integral technique to obtain a numerical description of the system, highlighting our proposed dissipation mechanism. In chapter 3 we will consider electron current pumping in a threesite system and how it can be affected by the presence of an environment. We will first obtain and solve a simple equation for the isolated system, then couple a bath to this and specialize the master equation theory to obtain an analytical result for the system in presence of an environment, observing some interesting changes it its behavior. The experimental feasibility of the proposed setup will be explored. Finally, in chapter 4 we will briefly present another model for the description of dissipative systems which has been investigated but, for now, is not complete enough to produce interesting results: inspired from another atomic force microscopy experiment where frictional effects of hydrogen atoms on a surface are observed, we will try to investigate the possibility of inherently quantum effects in a similar system, where a light particle is coupled to other heavier atoms, treated classically. We will propose a model and a technique for its simulation, though this will prove too computationally demanding to be of practical use.