12/1/2004

John Cardy
Oxford University and the Institute for Advanced Study

Quantum and Classical Network Models

In network models of transport, a particle moves along the edges and through the vertices of some fixed graph. In general, the classical and quantum versions of this problem are very different, the first being formulated in terms of transition probabilities, the second in terms of quantum-mechanical amplitudes. However, in some cases when the latter are random variables drawn from an ensemble, averaging the transport properties over this ensemble leads to an equivalent description in terms of a classical problem. In this talk I will illustrate this with some simple examples, then sketch the elements of the general proof, which uses supersymmetry.