Theoretical Approaches to Multi-Scale Complex Systems

Washington University, Saint Louis MO

Investigators

Abstract

NONTECHNICAL SUMMARY This award supports theoretical and data-centric computational research and education with an aim to advance the understanding of complex materials. In a perfect crystal, periodically repeating a fundamental structural unit of atoms can generate the entire atomic structure of the material. The theoretical description of such a structure of atoms leads to the elegant explanation of many properties of crystalline or near crystalline materials. By contrast, in complex materials such as glasses, additional rich structures appear on length scales between the atomic and the macroscopic scales. These features make understanding a wide range of materials from ordinary window glass to high temperature superconductors which can conduct electricity without resistance challenging. A goal of this project is to seek and quantify important structures in glassy materials - not by looking for particular known patterns- but rather by an unbiased analysis of structural data while invoking general physical principles. To address this challenge, the PI will broaden network analysis and computer vision methods to pinpoint and quantify the salient features of complex materials across different scales of length and time. This project will introduce new mathematical techniques for studying complex heterogeneous dynamics of both classical and quantum systems. The research will be done in close contact with experimental research groups around the world. The theoretical and data intensive computational study, in combination with experimental observations, is expected to lead to a deeper understanding of the structure of complex materials and systems including neural circuits, and enable progress in other disciplines. The techniques developed in this award will enhance cross-fertilization between condensed matter physics and other areas with multi-scale architectures such as medical imaging, bioinformatics, and communication networks. In collaboration with experimental neuroscientists, the PI aims to apply theoretical and data-centric computational tools developed in the course of research on materials to the visual neural circuits of the brain. This project supports training graduate students as well as further developing courses on advanced statistical mechanics and quantum information. The PI will also engage high school and undergraduate students to design software packages that illustrate the use of some of the methods developed during the course of the research. TECHNICAL SUMMARY This award supports theoretical and data-centric computational research and education in theoretical condensed matter physics of materials with complex structure. The PI aims to develop and explore a new framework involving empirical data combined with ideas from data mining and network theory, Fokker-Planck, and other methods, to systematically uncover natural structures across a broad range of spatial and temporal scales. Analysis of experimental data of structural glasses and complex electronic materials will be performed with the aid of methods developed in the course of the project. Research will, specifically, be conducted along several directions: (1) The PI aims to employ ideas from statistical mechanics and network theory to unveil natural building blocks in disparate complex materials. The analysis will be performed on both experimental and simulation results in various materials systems including metallic glass alloys and electronic systems. As a byproduct, new concepts and tools will be developed and applied to optimization as well as imaging problems of wide interest. In collaboration with neuroscientists, the PI plans to apply developed tools to the study of the structure of the circuitry of the visual system of the brain. (2) The project will probe for low temperature quantum dynamical heterogeneities in cuprate superconductors and other electronic systems through a direct analysis of experimental data. Novel quantum effects at high temperatures will be further investigated. (3) Fokker-Planck methods will be applied to the study of structure and evolution of viscous systems. (4) The PI will investigate the mechanical properties of complex systems, in particular how they may respond to external shear, and ascertain associated length scales. This project provides a multidisciplinary research environment and an opportunity for students to learn a multitude of valuable techniques, including: molecular dynamics, image and network analysis, and data mining, in the context of close connection to experiments. The PI aims to review and communicate current ideas in network science, statistical mechanics, and condensed matter physics to graduate students through new courses. He also plans to engage high school and undergraduate students to design software packages that illustrate the use of some of the methods developed during the course of the research.