Far From Equilibrium Dynamics

This book is devoted to the study of evolution of nonequilibrium systems. Such a system usually consists of regions with different dominant scales, which coexist in the space-time where the system lives. In the case of high nonuniformity in special direction, one can see patterns separated by clearly distinguishable boundaries or interfaces. The author considers several examples of nonequilibrium systems. One of the examples describes the invasion of the solid phase into the liquidphase during the crystallization process. Another example is the transition from oxidized to reduced states in certain chemical reactions. An easily understandable example of the transition in the temporal direction is a sound beat, and the author describes typical patterns associated with thisphenomenon. The main goal of the book is to present a mathematical approach to the study of highly nonuniform systems and to illustrate it with examples from physics and chemistry. The two main theories discussed are the theory of singular perturbations and the theory of dissipative systems. A set of carefully selected examples of physical and chemical systems nicely illustrates the general methods described in the book.

The proceedings discuss the theoretical methods used to describe a chemical system which is far from the equilibrium state, and this is illustrated by selected applications. Special attention is paid to very fast chemical reactions and systems in which external or internal noise is present. In particular, the following topics are covered:-the generalized Boltzmann/ Enskog equation for nonequilibrium systems,-stochastic methods for description of noise in chemical systems,-numerical simulations of systems far from equilibrium.

Originally published in 1991, this book, based on the 1989 Beg-Rohu summer school, contains six sets of pedagogical lectures by internationally respected researchers on the statistical physics of crystal growth. Providing a course in which the phenomena of shape and growth are viewed from a fresh vantage point, the lectures cover a variety of developments in the field and reflect on problems that have received inadequate attention. Statistical physicists, condensed matter physicists, metallurgists, and applied mathematicians will find this a stimulating and valuable book on an important topic.

This text gives a detailed account of various techniques that are used in the study of dynamics of continuous systems, near as well as far from equilibrium. The analytic methods covered include diagrammatic perturbation theory, various forms of the renormalization group, and self-consistent mode coupling.

This book deals with the formulation of the thermodynamics of chemical and other systems far from equilibrium. It contains applications to non-equilibrium stationary states and approaches to such states, systems with multiple stationary states, stability and equi-stability conditions, reaction diffusion systems, transport properties, and electrochemical systems. The theoretical treatment is complemented by experimental results to substantiate the formulation.

We consider the state of a one-dimensional critical quantum system after a \thermal cut-and-glue quench", which is a local quench in which two independently thermalized halves are connected to form a homogeneous in nite system and left to evolve unitarily until they reach a non-equilibrium steady state (NESS). This quench was studied in [1], and exact CFT results for the current and its uctuations in the NESS were found. We add to these results by studying the growth of entanglement after the quench. Furthermore, we generalise to the case in which the system is not critical, but described by an integrable relativistic quantum eld theory (IQFT) with diagonal scattering, and nd exact expressions for the energy current and scaled cumulant generating function (CGF) in the NESS. Another generalisation we consider is the thermal cut-and-glue quench for N independently thermalised critical one-dimensional systems. These are made to form a quantum junction consisting of N one-dimensional critical systems that are connected at one point in a star graph con guration, with a particular, simple connection condition at the vertex. We nd in this situation the exact energy current and scaled CGF in the NESS.

This monograph provides graduate students and also professional researchers aiming to understand the dynamics of open quantum systems with a valuable and self-contained toolbox. Special focus is laid on the link between microscopic models and the resulting open-system dynamics. This includes how to derive the celebrated Lindblad master equation without applying the rotating wave approximation. As typical representatives for non-equilibrium configurations it treats systems coupled to multiple reservoirs (including the description of quantum transport), driven systems and feedback-controlled quantum systems. Each method is illustrated with easy-to-follow examples from recent research. Exercises and short summaries at the end of every chapter enable the reader to approach the frontiers of current research quickly and make the book useful for quick reference.