2026-09-19T03:49:05Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/1140782026-06-16T18:16:34Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Roy E. Welsch.
Xie, Wanqin, Ph. D. Massachusetts Institute of Technology
Massachusetts Institute of Technology. Department of Chemistry.
Massachusetts Institute of Technology. Department of Chemistry
2018-03-12T19:28:56Z
2018-03-12T19:28:56Z
2017
2017
http://hdl.handle.net/1721.1/114078
1027215949
Thesis: Ph. D. in Physical Chemistry, Massachusetts Institute of Technology, Department of Chemistry, 2017.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 72-77).
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.
by Wanqin Xie.
Ph.D. in Physical Chemistry
77 pages
eng
Massachusetts Institute of Technology
MIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission.
http://dspace.mit.edu/handle/1721.1/7582
Chemistry.
Application of RMT-RNN improved decomposition onto defected system
Application of Random Matrix Theory coupled with Neural Networks improved decomposition onto defected system
Thesis
application/pdf
Publication
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<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.</Abstract>
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