Quantum Network Models and Classical Localization Problems

Details Quantum Network Models and Classical Localization Problems Quantum Network Models and Classical Localization Problems

2010-04-19

arxiv.org/abs/1004.3198v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

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

Scientific paper

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.

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