Theoretical Approaches to Multi-Scale Complex Systems

Washington University, Saint Louis MO

Investigators

Abstract

TECHNICAL SUMMARY This award supports research and education in theoretical condensed matter physics aimed at revealing the potentially complex structure of materials. The PI will use ideas from statistical mechanics and network theory to reveal natural structures in various materials across spatial and temporal scales. Analysis of experimental data of structural glasses as well as complex electronic materials will be performed with the aid of methods developed in the course of the research. The research has two thrusts: (1) In complex materials there are in general possibly many important length and time scales that characterize correlations. Aside from multiple correlation lengths describing the exponential decay of correlations, in some materials there are length scales that characterize periodic spatial or temporal modulations. The PI will investigate the evolution of these length scales as a function of temperature and other parameters. (2) The PI will demonstrate the existence of quantum dynamical heterogeneities in electronic systems, similar to those in classical glass formers. The PI will establish the existence of such heterogeneities via mapping to classical models and methods to analyze experimental data. This award also supports training a postdoctoral research associate and a graduate student as well as the 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 techniques to be developed during the course of the research. NONTECHNICAL SUMMARY This award supports research and education in theoretical condensed matter physics for the discovery of subtle hidden structures in complex materials. Currently, there are no universal tools for examining complex physical systems in a general and systematic way that reveal their pertinent features from the smallest fundamental unit to the largest scale encompassing the entire system. In a perfect crystal, a fundamental structure of atoms, called a unit cell, can be replicated to reproduce the structure of the entire system. This concept enables a fundamental understanding of many solid materials in great detail. In complex systems and materials, rich new structures appear on additional intermediate scales. Some of the oldest and, after several millennia, still heavily investigated materials are glasses. More recent challenges include the high temperature superconductors and heavy fermion compounds that exhibit a rich array of behavior including superconductivity, wherein electrical current flows without resistance, and complicated magnetic characteristics. It is often unclear which of the many features of these kinds of physical systems holds the key to understanding certain properties or phenomena in these materials. Hypothesized models often fail to provide an adequate or even qualitatively correct description of important properties of phenomena. The PI aims to develop innovative methods that pinpoint important features and enable progress by regarding complex materials and physical systems as large networks and employing tools from network analysis to flesh out their essential features across scales of time and length. This award also supports training a postdoctoral research associate and a graduate student as well as the 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 techniques to be developed during the course of the research.