Random matrix theory for CPA: Generalization of Wegner’s \(n\)-orbital model. (English) Zbl 0857.60098
Summary: We introduce a generalization of Wegner’s \(n\)-orbital model for the description of randomly disordered systems by replacing his ensemble of Gaussian random matrices by an ensemble of randomly rotated matrices. We calculate the one- and two-particle Green functions and the conductivity exactly in the limit \(n \to \infty\). Our solution solves the coherent potential approximation equation of the \((n = 1)\) Anderson model for arbitrary distributed disorder. We show how the Lloyd model is included in our model.
MSC:
60K40 | Other physical applications of random processes |
82B31 | Stochastic methods applied to problems in equilibrium statistical mechanics |
81S30 | Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics |