RANDOM-MATRIX THEORY OF QUANTUM TRANSPORT

This is a review of the statistical properties of the scattering matri x of a mesoscopic system. Two geometries are contrasted: A quantum dot and a disordered wire. The quantum dot isa confined region with a cha otic classical dynamics, which is coupled to two electron reservoirs v ia point contacts. The disordered wire also connects two reservoirs, e ither directly or via a point contact or tunnel barrier. One of the tw o reservoirs may be in the superconducting state, in which case conduc tion involves Andreev reflection at the interface with the superconduc tor. In the case of the quantum dot, the distribution of the scatterin g matrix is given by either Dyson's circular ensemble for ballistic po int contacts or the Poisson kernel for point contacts containing a tun nel barrier, In the case of the disordered wire, the distribution of t he scattering matrix is obtained from the Dorokhov-Mello-Pereyra-Kumar equation, which is a one-dimensional scaling equation, The equivalenc e is discussed with the nonlinear sigma model, which is a supersymmetr ic field theory of localization. The distribution of scattering matric es is applied to a variety of physical phenomena, including universal conductance fluctuations, weak localization, Coulomb blockade, sub-Poi ssonian shot noise, reflectionless tunneling into a superconductor, an d giant conductance oscillations in a Josephson junction.