Quantum Network Models and Classical Localization Problems

Abstract

A review is given of quantum network models in class C which, on a suitable 2d lattice, describe the spin quantum Hall plateau transition. On a general class of graphs, however, many observables of such models can be mapped to those of a classical walk in a random environment, thus relating questions of quantum and classical localization. In many cases it is possible to make rigorous statements about the latter through the relation to associated percolation problems, in both two and three dimensions.

23 pages. To appear in '50 years of Anderson Localization', E Abrahams, ed. (World Scientific).

References in corpus (3)

• Quantum and classical localisation, the spin quantum Hall effect and generalisations
• Random Walks and Anderson Localisation in a Three-Dimensional Class C Network Model
• Network Models in Class C on Arbitrary Graphs

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