Abstract

Localisation of a particle moving in a random environment may occur both quantum mechanically and with classical dynamics, but the phenomenon is very different in the two cases. I will discuss a class of quantum-mchanical localisation problems for which some physical quantities can be expressed exactly in terms of averages taken in a classical counterpart. The equivalence holds despite the fact that interference effects dominate the behaviour of the quantum systems. The models are network models belonging to class C in Zirnbauer’s classification. The equivalence was first discovered in the context of the spin quantum Hall effect by Gruzberg, Ludwig and Read [Phys. Rev. Lett. 82, 4524 (1999)], and the results I will describe were obtained in collaboration with Beamond and Cardy [Phys Rev B 65 , 214301 (2002) and with Ortuno and Somoza [in preparation].