Quantum particles and Gaussian model on graphs

A quantum particle on a general discrete structure with a local external po tential is described by a generalized tight-binding Hamiltonian on a graph. Here, we show that this model can be naturally mapped on a classical stati stical model (the Gaussian model) on the same graph. This equivalence provi des not only a powerful technical tool for model solving, but it also puts into evidence general fundamental properties of quantum inhomogeneous syste ms. (C) 2000 Published by Elsevier Science B.V. All rights reserved.