Statistical Mechanics of Systems far from Equilibrium

Virginia Polytechnic Institute And State University, Blacksburg VA

Investigators

Abstract

0088451 Schmittmann This grant supports theoretical research on systems far from thermal equilibrium. The goal is the characterization and understanding of complex behavior in interacting many-particle systems, driven into steady states far from thermal equilibrium. A combination of computational and analytical techniques, formulated on the lattice or the continuum, will be brought to bear on various systems, from Ising-like models to selected experiments. In contrast to Gibbsean ensemble theory, there is as yet no fundamental theoretical framework for a comprehensive classification of nonequilibrium phenomena. Even the study of nonequilibrium steady states, being the simplest generalizations of equilibrium states, is far from complete. Given the ubiquity of such states in a broad range of physical systems, formulating a theory with predictive power remains one of the key challenges of condensed matter physics. Seeking to characterize generic large scale properties and universal behavior, the focus will be on minimal model systems of the Ising type, inspired by the successful role which the latter played in equilibrium statistical mechanics. An external drive, suitably applied, prevents such systems from reaching equilibrium; instead, they settle into nonequilibrium steady states. Energy is injected by the drive and absorbed by the thermal bath so that a non-trivial, steady through-flux is established. Such systems display much richer phenomena than their equilibrium cousins, including generic long-range correlations, novel nonequilibrium phase transitions and unexpected ordered structures. Significant insights have been gained, illustrating the key role played by global currents and basic symmetries, e.g., detailed balance and conservation laws. In contrast to equilibrium systems, however, the dynamics inherently affects steady state properties, so that even minor modifications of the microscopic rules can affect macroscopic behavior in profound, entirely unanticipated ways. The challenge is to craft a reliable theoretical picture which can serve as a guide from the microscopic to the macroscopic. In the first part of the research, investigations will continue on collective behavior of driven lattice gases. Despite their apparent simplicity, these models provide a variety of complex phenomena and pose new challenges. Examples include shape-dependent thermodynamics, new universality classes of critical behavior, anomalous interfacial correlations, novel phases, and peculiar domain growth. Further investigations of these simple models should furnish steps toward the long-range goal: a meaningful classification of macroscopic nonequilibrium steady states based on their underlying dynamics. The second part of the research introduces three new pursuits: polymer crystallization, granular materials, and population dynamics. Governed by nonequilibrium dynamics, these phenomena have been extensively studied experimentally. Being physical systems, these are clearly much more complex than driven Ising models. However, the tools used here, honed in the study of simple models, should serve well in analyzing experimental data and understanding the essence of these systems. In both parts of the research, projects range from well-defined, short-term studies, for which progress is certain, to long-term ventures involving more fundamental and complex issues. Although they require substantial thought and time, the problems in the latter category deserve attention, since they promise deeper insights into the general nature of nonequilibrium steady states. %%% This grant supports theoretical research on systems far from thermal equilibrium. The goal is the characterization and understanding of complex behavior in interacting many-particle systems, driven into steady states far from thermal equilibrium. A combination of computational and analytical techniques, formulated on the lattice or the continuum, will be brought to bear on various systems, from Ising-like models to selected experiments. ***