Random Network Models and Quantum Phase Transitions in Two Dimensions

An overview of the random network model invented by Chalker and Coddington, and its generalizations, is provided. After a short introduction into the physics of the Integer Quantum Hall Effect, which historically has been the motivation for introducing the network model, the percolation model for electrons in spatial dimension 2 in a strong perpendicular magnetic field and a spatially correlated random potential is described. Based on this, the network model is established, using the concepts of percolating probability amplitude and tunneling. Its localization properties and its behavior at the critical point are discussed including a short survey on the statistics of energy levels and wave function amplitudes. Magneto-transport is reviewed with emphasis on some new results on conductance distributions. Generalizations are performed by establishing equivalent Hamiltonians. In particular, the significance of mappings to the Dirac model and the two dimensional Ising model are discussed. A description of renormalization group treatments is given. The classification of two dimensional random systems according to their symmetries is outlined. This provides access to the complete set of quantum phase transitions like the thermal Hall transition and the spin quantum Hall transition in two dimension. The supersymmetric effective field theory for the critical properties of network models is formulated. The network model is extended to higher dimensions including remarks on the chiral metal phase at the surface of a multi-layer quantum Hall system.Comment: 176 pages, final version, references correcte

Fine-grain process modelling

In this paper, we propose the use of fine-grain process modelling as an aid to software development. We suggest the use of two levels of granularity, one at the level of the individual developer and another at the level of the representation scheme used by that developer. The advantages of modelling the software development process at these two levels, we argue, include respectively: (1) the production of models that better reflect actual development processes because they are oriented towards the actors who enact them, and (2) models that are vehicles for providing guidance because they may be expressed in terms of the actual representation schemes employed by those actors. We suggest that our previously published approach of using multiple “ViewPoints” to model software development participants, the perspectives that they hold, the representation schemes that they deploy and the process models that they maintain, is one way of supporting the fine-grain modelling we advocate. We point to some simple, tool-based experiments we have performed that support our proposition

Numerical study on Anderson transitions in three-dimensional disordered systems in random magnetic fields

The Anderson transitions in a random magnetic field in three dimensions are investigated numerically. The critical behavior near the transition point is analyzed in detail by means of the transfer matrix method with high accuracy for systems both with and without an additional random scalar potential. We find the critical exponent $\nu$ for the localization length to be $1.45 \pm 0.09$ with a strong random scalar potential. Without it, the exponent is smaller but increases with the system sizes and extrapolates to the above value within the error bars. These results support the conventional classification of universality classes due to symmetry. Fractal dimensionality of the wave function at the critical point is also estimated by the equation-of-motion method.Comment: 9 pages, 3 figures, to appear in Annalen der Physi

Dynamics of a large-spin-boson system in the strong coupling regime

We investigate collective effects of an ensemble of biased two level systems interacting with a bosonic bath in the strong coupling regime. The two level systems are described by a large pseudo-spin J. An equation for the expectation value M(t) of the z-component of the pseudo spin is derived and solved numerically for an ohmic bath at T=0. In case of a large cut-off frequency of the spectral function, a Markov approximation is justified and an analytical solution is presented. We find that M(t) relaxes towards a highly correlated state with maximum value $\pm J$ for large times. However, this relaxation is extremely slow for most parameter values so as if the system was "frozen in" by interaction with the bosonic bath.Comment: 4 pages, 2 figures, to be published in proceedings of MB1