Free approximation of transport properties in organic system using Stochastic Random Matrix Theory

Abstract

The proposed research is a study and application of Stochastic analysis- Random Matrix Theory(RMT) to fast calculate the transport properties of large static systems with relatively large disorder in mesoscopic size. As a major topic of Random Matrix Theory(RMT), free convolution managed to approximate the distribution of eigenvalues in an Anderson Model.So the next step is trying to expand RMT to approximate other quantities, such as transmission probability, conductivity and etc. Due to the eigenvectors' shifts, RMT works well only for small disorder. System with larger disorder requires to take in account of the changes in eigenvectors directly or through other approximations of the eigenvectors.