Electronic relaxation and dissipation in mesoscopic systems

This thesis is concerned with the theoretical study of the transport in small conductors at low temperatures. Our aim is to elucidate the interplay between the statistical environment and mesoscopic systems, and its effect on electronic features in the domain of transport. In a first phenomenological approach based on the Landauer picture of transport, we study de transport properties of a mesoscopic sample connected to electronic reservoirs. The influence of the coupling to the statistical environment on the phase-coherence time and on the conductance of an electronic open system is then investigated. Our results may explain recent experimental findings showing the saturation of the phase-coherence time at low temperatures and the emergence of nonuniversal conductance steps in perfect quantum wires. We present a microscopic model to account for the coupling between small finite electronic systems and the further environment via local vibrational degrees of freedom. We calculate the time-evolution of the density matrix of the sample system, by applying a simple iterative procedure. Using this approach, the energy relaxation of electrons in a one-dimensional loop is studied and the role of the electron-electron interaction and the coupling to the environment is discussed. We analyse currents in a loop, which is threaded by a constant magnetic flux, and compare our results with the common ground state theory of the persistent currents. Our model is extended to describe the situation of a loop, in which the electrons are driven by a time-dependent magnetic field. In particular, we study the electronic current in the presence as well as in the absence of dissipation. In this description, both coherent and dissipative processes are uniformly distributed in the loop system, in contrast with the Landauer approach to dc transport, where dissipative and coherent regions are spatially separated.