Statics and Dynamics of Materials with Quenched Disorder

Syracuse University, Syracuse NY

Investigators

Abstract

This project is a theoretical exploration of material systems that are controlled by disorder. Disorder is prevalent in materials and is central to experiments ranging from electronic transport in porous conductors or nanoscopic dot arrays through the dynamics of colloidal systems and of domain walls in magnetic films. The principal investigator ( PI) will carry out extensive numerical simulations using models of (1) inhomogeneous magnets and interfaces with competing interactions and (2) the flow of particles in materials with random pinning. The PI will also pursue a better description the apparent connections between the algorithms used to study disordered materials and the theoretical pictures of the models. These strands link computer science methods and physical pictures, which share a fundamental mathematical basis in graph theory and statistical mechanics. Intellectual merit: The description of materials by coarse-grained models, which capture the essential energetics and dynamics using (mostly) classical degrees of freedom, has provided fundamental insight into the phases and dynamics of condensed matter. Simulations of such models provide both quantitative predictions and qualitative descriptions; they are especially needed for understanding the collective behavior of disordered materials, for which clear analytic answers are often lacking. The PI has studied and developed optimization algorithms to study the low temperature behavior of such models for disordered magnets, such as the random field Ising magnet and spin glasses, and will improve simulations to build more coherent pictures of disordered systems. The PI will also develop new schemes for computing barriers to relaxation and accelerating the dynamics of glassy systems, in order to study aging and memory effects over a wide range of time scales. Better understanding of algorithms for studying ground states and dynamics will be closely linked to physical pictures of these models. The study of transport in condensed matter systems encompasses many distinct problems, depending on whether quantum effects are important, the role of temperature, the strength of the interactions, etc. The PI will study the set of problems relevant to degrees of freedom that are best described at the mesoscopic scale, where quantum effects are negligible and the temperature is not large. Such problems include the transport of electrons between arrays of small particles, viscous fluids in porous media, and magnetic vortices in superconductors. An anisotropic coarse-grained model, developed by the PI and collaborators for studying plastic flow with conservation laws, will be studied in detail. In addition to investigating randomness in these systems, the PI will simulate the response of designed quasiperiodic systems to ac drives, such as might be realized with colloidal particles. Broader impact: Progress on the specific scientific goals of this project will be closely connected with more general benefits. The PI will train graduate students and postdoctoral researchers, with an important focus on the overlap between direct simulation, advanced algorithms, and condensed matter physics. The models to be studied are prototypes for disordered materials and have inspired physical pictures for a wide range of systems, including quantum critical points in the presence of disorder and the folding of biopolymers. Progress on understanding the statics and dynamics of disordered systems, including domain structure and hysteresis, has eventual application to materials development, including magnetic memories. This work will strengthen connections between ideas in computer science (algorithms for combinatorial optimization and their running time) and physics (lengths scales and dynamics infinite-dimensional materials). The computer programs developed by the PI will be made generally available. The PI is active in sharing science with the local community through presentations and activities related to condensed matter physics. Non-Technical Abstract: This theoretical project will explore materials and condensed systems whose properties are determined by disorder. Classic solid state materials are characterized by atoms arranged in perfect order. Yet most materials have some degree of disorder and some owe their unique properties to the presence of disorder. This research will use primarily numerical methods (computation) to study the effects of disorder on a variety of materials of current interest. The connection between the numerical methods used and the physical picture described can lead to advances in computer codes that have wider application. These connections will also be pursued.