Open Mesoscopic Systems: beyond the Random Matrix Theory

Abstract

Physical systems having sizes between microscopic and macroscopic are referred to as mesoscopic. The motion in mesoscopic systems is phase-coherent, that means they must be treated by quantum mechanics. Another important property of mesoscopic systems is that they usually contain a lot of microscopic details (e.g. an impurity arrangement) which can not be taken into account exactly. Therefore one chooses a statistical approach considering an ensemble of systems having different microscopic configurations but the same macroscopic parameters. The rapid development of technology of fabrication of small electronic structures, having dimensions from a few nanometers to hundreds of microns, allows now to study mesoscopic systems experimentally.In experiments or measurements one deals not with idealized closed, but with open systems. The natural way to describe an open system in quantum mechanics is to use a scattering formalism. Statistical approach to the scattering problems in mesoscopic physics is usually based on the random matrix theory (RMT). The strength of the RMT consists in the universality of its predictions containing no energy or length scales or any parameter dependence. At the same time this is the weakness of the RMT, because it does not allow to take into account various phenomena appearing in mesoscopic systems, which introduce new scales or parameters in the system, like for example localization.This thesis is devoted to study exactly that type of scattering problems where "naive" RMT can not be applied. We consider different models of disordered and chaotic systems whose closed analogs have various specific features such as diffusion, fractality or localization. The investigation of different quantities related to scattering, like distributions of the Wigner delay times and the resonance widths, the survival probability, allows us to show how these features manifest themselves in the statistical properties of open systems.