This award supports theoretical studies of non-equilibrium condensed matter systems. Statistical mechanics provides the foundation for our present understanding of interacting many-particle systems. In the (usually idealized) situation of thermal equilibrium, the probability distributions for a variety of physical realizations are known at least in principle. This allows a systematic construction of the thermodynamics of a given system in terms of a few relevant macroscopic variables, and the derivation of its equations of state. For systems slightly disturbed away from equilibrium, linear response theory can be used to compute dynamical susceptibilities, transport coefficients, and relaxation rates.
However, no such general theoretical framework exists to date for systems far from equilibrium. Aside from a large variety of interesting physical examples, many chemical and virtually all biological systems are sustained in a non-equilibrium steady state (NESS). In addition, problems from ecology, sociology, and economic theory can be described in terms of stochastic processes, i.e., models akin to those used in non-equilibrium statistical mechanics. Among the truly fundamental problems in current theoretical physics is therefore the characterization of the stationary probability distributions of NESS in terms of certain global properties such as symmetries, overall features of the interactions, conservation laws, etc. Some progress in this direction has been achieved for non-equilibrium systems that are either tuned to the vicinity of a dynamic phase transition, or generally display scale invariance: In these situations the renormalization group (RG) can be employed as a powerful tool to classify the ensuing phases and characterize the transitions in terms of universal scaling properties.
Based on previous research, the project here has a double approach to the investigation of NESS in scale-invariant dynamical systems, namely the study of simplified model cases by means of all available mathematical methods, and the detailed analysis of experiments performed far-from-equilibrium conditions. The goal is to extract general features and principles that permit the classification of NESS and, in the second case, optimize material properties and processes.
The project offers an integrated interdisciplinary environment for research and education. Research material will be incorporated into courses. A textbook on this subject continues to be written. %%% This theoretical research project addresses the non-equilibrium behavior of condensed matter systems. Typical examples of such systems are materials growth, pattern formation, and phase transitions with driving forces. Most chemical systems and all biological systems are in these non-equilibrium states. Research will look for common themes that can assist the understanding of these phenomena.
The project offers an integrated interdisciplinary environment for research and education. Research material will be incorporated into courses. A textbook on this subject continues to be written. ***
