Steady state properties of discrete and continuous models of nonequilibrium phenomena

Abstract

The understanding of nonequilibrium phenomena, of fundamental importance in statistical physics, has great implications for many physical, chemical, and biological systems. Such phenomena are observed almost everywhere in the natural world. These phenomena are characterized by complicated spatiotemporal evolution. To explore nonequilibrium phenomena we often study simple model systems that embody their essential characteristics. In this thesis, we report the results of our investigations of the statistically steady state properties of three one-dimensional models: multispecies asymmetric simple exclusion processes, the Kuramoto- Sivashinsky equation, and the Burgers equation. The thesis is divided into two parts: Part I and Part II. In Chapters 2 5 of Part I, we present our results for multispecies exclusion models, principally the phase diagrams and statistical properties of their nonequilibrium steady state (NESS). We list below abstracts of these chapters. In Chapter 2, we consider a multispecies ASEP (mASEP) on a one-dimensional lattice with semipermeable boundaries in contact with particle reservoirs. The mASEP involves ¹2and#119903; ¸1º species of particles: and#119903; species of positive charges and their negative counterparts as well as vacancies. At the boundaries, a species can replace or be replaced by its negative counterpart. We derive the exact nonequilibrium phase diagram for the system in the long time limit. We find two new phenomena in certain regions of the phase diagram: dynamical expulsion when the density of a species becomes zero throughout the system, and dynamical localization when the density of a species is nonzero only within an interval far from the boundaries. We give a complete explanation of the macroscopic features of the phase diagram using what we call nested fat shocks. In Chapter 3, we study an asymmetric exclusion process with two species and vacancies on an open one-dimensional lattice called the left-permeable ASEP (LPASEP)...