This document provides a review of random matrix theory and its application to quantum transport in mesoscopic systems. It summarizes the key results in four areas: (1) the statistical properties of energy levels in quantum dots are described by random matrix ensembles like the circular orthogonal ensemble; (2) transport properties of quantum dots can be understood from the distribution of scattering matrices; (3) transport in disordered wires is described by the Dorokhov-Mello-Pereyra-Kumar equation which yields the distribution of transmission eigenvalues; (4) scattering theory can be applied to normal-metal-superconductor junctions to understand phenomena like Andreev reflection and universal conductance fluctuations. The document serves as an overview

Random-Matrix Theory of Quantum Transport: Instituut-Lorentz, University of Leiden 2300 RA Leiden, The Netherlands PDF

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