On the basis of the Chalker-Coddington network model, a numerical and analytical study is made of the statistics of point-contact conductances for systems in the integer quantum Hall regime. In the Hall plateau region the point-contact conductances reflect strong localization of the electrons, while near the plateau transition they exhibit strong mesoscopic fluctuations. By mapping the network model on a supersymmetric vertex model with GL(2͉2) symmetry, and postulating a two-point correlator in keeping with the rules of conformal field theory, we derive an explicit expression for the distribution of conductances at criticality. There is only one free parameter, the power law exponent of the typical conductance. Its value is computed numerically to be X t ϭ0.640Ϯ0.009. The predicted conductance distribution agrees well with the numerical data. For large distances between the two contacts, the distribution can be described by a multifractal spectrum solely determined by X t . Our results demonstrate that multifractality can show up in appropriate transport experiments.

We investigate numerically the localization-delocalization transition in quantum Hall systems with long-range disorder potential with respect to multifractal properties. Wave functions at the transition energy are obtained within the framework of the generalized Chalker-Coddington network model. We determine the critical exponent a. characterizing the scaling behaviour of the local order parameter for systems with potential correlation length d up to 12 magnetic lengths 1. Our results show that a. does not depend on the ratio d/l. With increasing d/l, effects due to classical percolation only cause an increase of the microscopic length scale, whereas the critical behaviour on larger scales remains unchanged. This proves that systems with long-range disorder belong to the same universality class as those with short-range disorder.

The spectral properties of a disordered electronic system at the metal-insulator transition point are investigated numerically. A recently derived relation between the anomalous diffusion exponent h and the spectral compressibility x at the mobility edge, x h͞2d, is confirmed for the integer quantum Hall delocalization transition. Our calculations are performed within the framework of a unitary network model and represent a new method to investigate spectral properties of disordered systems.[S0031-9007(97)

The ability to process visual information using relational rules allows for decisions independent of the specific physical attributes of individual stimuli. Until recently, the manipulation of relational concepts was considered as a prerogative of large mammalian brains. Here we show that individual free flying honeybees can learn to use size relationship rules to choose either the larger or smaller stimulus as the correct solution in a given context, and subsequently apply the learnt rule to novel colors and shapes providing that there is sufficient input to the long wavelength (green) photoreceptor channel. Our results add a novel, size-based conceptual rule to the set of relational concepts that honeybees have been shown to master and underline the value of bees as an animal model for studying the emergence of conceptualization abilities.