Application of RMT-RNN improved decomposition onto defected system

Abstract

This thesis is about the study and application of a stochastic optimization algorithm - Random Matrix Theory coupled with Neural Networks (RMT-RNN) to large static systems with relatively large disorder in mesoscopic systems. It is a new algorithm that can quickly decompose random matrices with real eigenvalues for further study of physical properties, such as transmission probability, conductivity and so on. As a major topic of Random Matrix Theory (RMT), free convolution has managed to approximate the distribution of eigenvalues in the Anderson Model. RMT has proven to work well when looking for the transport properties in slightly defect system. Systems with larger disorder require to take in account of the changes in eigenvectors as well. Hence, combined with parallelizable Neural Network (RNN), RMT-RNN turns out to be a great approach for eigenpair approximation for systems with large defects.