Scattering theory and conductance fluctuations in mesoscopic systems

A random-matrix model developed originally in the framework of the statistical theory of nuclear reactions is (via the many-channel approximation of Landauer's formula) applied to universal conductance fluctuations (UCF) in a disordered sample connected to two or three leads. The leads are modelled as ideal conductors. For large sample lengths, the results agree with those obtained by other approaches. This shows that UCF can be modelled successfully in terms of random matrices. For sample lengths of several tens of elastic mean free paths, the conductance fluctuations are seen to depend sensitively on the coupling to the leads. This is due to the appearance of a new energy scale, the width Γ for emission of an electron from the disordered sample into the leads. This quantity Γ also influences the autocorrelation function of the conductance. Results are presented for the three canonical random-matrix ensembles: The Gaussian orthogonal, unitary, and symplectic ensembles.