Random-matrix approach to the quantum-transport theory of disordered conductors

Turbulence Hierarchy and Multifractality in the Integer Quantum Hall Transition

We offer a new perspective on the problem of characterizing mesoscopic fluctuations in the interplateau regions of the integer quantum Hall transition. We found that longitudinal and transverse conductance fluctuations, generated by varying the external magnetic field within a microscopic model, are multifractal and lead to distributions of conductance increments (magnetoconductance) with heavy tails (intermittency) and signatures of a hierarchical structure (cascade) in the corresponding stochastic process, akin to Kolmogorov's theory of fluid turbulence. We confirm this picture by interpreting the stochastic process of the conductance increments in the framework of H theory, which is a continuous-time stochastic approach that incorporates the basic features of Kolmogorov's theory. The multifractal analysis of the conductance "time series," combined with the H-theory formalism, provides strong support for the overall characterization of mesoscopic fluctuations in the quantum Hall transition as a multifractal stochastic phenomenon with multiscale hierarchy, intermittency, and cascade effects.

Conductance distributions in quasi-one-dimensional disordered wires

A detailed analysis of the distribution of conductances P(g) of quasi-one-dimensional disordered wires in the metal-insulator crossover is presented. P(g) obtained from a Monte Carlo solution of the Dorokhov, Mello, Pereyra, and Kumar (DMPK) scaling equation is in full agreement with "tight-binding" numerical calculations of bulk disordered wires. Perturbation theory is shown to be valid even for mean dimensionless conductances <g> of the order of 1. In the crossover regime <g> <, similar 1, P(g) presents a sharp feature at g=1 which is different from that observed in surface disordered wires.

Anomalous conductance distribution in quasi-one-dimensional gold wires: possible violation of the one-parameter scaling hypothesis

We report measurements of conductance distribution in a set of quasi-one-dimensional gold wires. The distribution includes the second cumulant or the variance which describes the universal conductance fluctuations, and the third cumulant which denotes the leading deviation. We have observed an asymmetric contribution--or, a nonvanishing third cumulant--contrary to the expectation for quasi-one-dimensional systems in the noninteracting theories in the one-parameter scaling framework, which include the perturbative diagrammatic calculations and the random matrix theory.