Dynamics Models And Kinetic Methods For Non Equilibrium Many Body Systems

Recent years have witnessed a resurgence in the kinetic approach to dynamic many-body problems. Modern kinetic theory offers a unifying theoretical framework within which a great variety of seemingly unrelated systems can be explored in a coherent way. Kinetic methods are currently being applied in such areas as the dynamics of colloidal suspensions, granular material flow, electron transport in mesoscopic systems, the calculation of Lyapunov exponents and other properties of classical many-body systems characterised by chaotic behaviour. The present work focuses on Brownian motion, dynamical systems, granular flows, and quantum kinetic theory.

The 1995 observation of Bose–Einstein condensation in dilute atomic vapours spawned the field of ultracold, degenerate quantum gases. Unprecedented developments in experimental design and precision control have led to quantum gases becoming the preferred playground for designer quantum many-body systems. This self-contained volume provides a broad overview of the principal theoretical techniques applied to non-equilibrium and finite temperature quantum gases. Covering Bose–Einstein condensates, degenerate Fermi gases, and the more recently realised exciton–polariton condensates, it fills a gap by linking between different methods with origins in condensed matter physics, quantum field theory, quantum optics, atomic physics, and statistical mechanics. Thematically organised chapters on different methodologies, contributed by key researchers using a unified notation, provide the first integrated view of the relative merits of individual approaches, aided by pertinent introductory chapters and the guidance of editorial notes. Both graduate students and established researchers wishing to understand the state of the art will greatly benefit from this comprehensive and up-to-date review of non-equilibrium and finite temperature techniques in the exciting and expanding field of quantum gases and liquids. Contents:Introductory Material:Quantum Gases: The BackgroundQuantum Gases: Experimental ConsiderationsQuantum Gases: Background Key Theoretical NotionsUltracold Bosonic Gases: Theoretical Modelling:Kinetic and Many-Body ApproachesClassical-Field, Stochastic and Field-Theoretic ApproachesComparison of Common TheoriesOverview of Related Quantum-Degenerate Systems:Nearly Integrable One-Dimensional SystemsOptical Lattice GeometriesLiquid HeliumDegenerate Fermi GasesExciton/Polariton Condensation Readership: Aimed at graduate level students and for researchers. Keywords:Quantum Gas;Bose–Einstein;Condensate;Mean Field;Classical Field;Quantum Dynamics;Cold Atom;Ultracold Atom;Superfluid;Non-Equilibrium;Kinetic Theory;Field Theory;Quantum Fluid;Quantum Liquid;Degenerate Gas;Quantum Statistics;Number-Conserving;Symmetry-Breaking;Finite Temperature;Fluctuations;Stochastic;Gross–Pitaevskii;Bogoliubov;Many Body;Phase-Space Methods;Low-Dimensional;Optical Lattice;Bose;Fermi;Exciton;Polariton;ThermalizationKey Features:This book provides a unique and editorially linked, impartial unified presentation of the leading theoretical models for quantum gases far from equilibrium, and at finite temperaturesIn addition to focusing on bosonic gases, this book also makes connections to related quantum gases and fluids, such as fermionic gases, atoms in optical lattices, as well as exciton and polariton condensatesIntroductory chapters make this book an essential, accessible resource to both graduate students and early researchers as well as established scientists, with individual chapters written and edited by prominent researchers in the fieldReviews:“This book should be the first reference point for learning about various theoretical approaches to describing quantum gases. The editors and contributors have created a unique book with well-written articles, meaningful comparisons of various approximation schemes, a uniform notation and more than one thousand references. In addition, the book features introductory chapters and up-to-date review articles of experimental methods and current frontiers. The completeness and depth of the presentation are impressive.”Wolfgang Ketterle, MIT-Harvard Center for Ultracold Atoms & Nobel Laureate

A comprehensive overview of recent progress in nonequilibrium statistical mechanics, including applications across a range of disciplines.

The book is devoted to the study of the correlation effects in many-particle systems. It presents the advanced methods of quantum statistical mechanics (equilibrium and nonequilibrium), and shows their effectiveness and operational ability in applications to problems of quantum solid-state theory, quantum theory of magnetism and the kinetic theory. The book includes description of the fundamental concepts and techniques of analysis following the approach of N N Bogoliubov's school, including recent developments. It provides an overview that introduces the main notions of quantum many-particle physics with the emphasis on concepts and models. This book combines the features of textbook and research monograph. For many topics the aim is to start from the beginning and to guide the reader to the threshold of advanced researches. Many chapters include also additional information and discuss many complex research areas which are not often discussed in other places. The book is useful for established researchers to organize and present the advanced material disseminated in the literature. The book contains also an extensive bibliography. The book serves undergraduate, graduate and postgraduate students, as well as researchers who have had prior experience with the subject matter at a more elementary level or have used other many-particle techniques.

This book contains accounts of state-of-the art approaches to the physics of granular matter, from a widely interdisciplinary and international set of experts in the field. The authors include theorists such as S F Edwards, J Krug and J Kurchan; the book is also unique in reporting current experimental approaches with, importantly, a detailed account of new techniques. It will serve as an invaluable handbook for all researchers, both novice and experienced, who wish to get quickly directed to open questions in key aspects of this challenging and topical domain. Contents:Models of Free Cooling Granular Gases (U M B Marconi et al.)The Steady State of the Tapped Ising Model (D S Dean & A Lefevre)Coarsening of Vortex Ripples in Sand (J Krug)Dense Granular Media as Athermal Glasses (J Kurchan)Liquid-Solid Transition in Bidisperse Granulates (S Luding)Surface Granular Flows: Two Related Examples (D V Khakhar et al.)Glassy States in a Shaken Sandbox (P F Stadler et al.)Granular Media as a Physics Problem (S F Edwards & D V Grinev)Nonlinear Elasticity and Thermodynamics of Granular Materials (H A Makse)Granular Flow Studies by NMR: A Chronology (E Fukushima)Random Multiplicative Response Functions in Granular Contact Networks (C F Moukarzel)and other papers Readership: Students, researchers, academics and scientists working in industry. Keywords:Granular;Glassy;Compaction;Random;Vibrated Sand;Dense Flows;Dynamics;Complex Systems;Wet Sand;Soft Matter;Thermodynamics;Fragile Matter;Matter Under Shear;Avalanches;Ripples;NMR

A valuable introduction for newcomers as well as an important reference and source of inspiration for established researchers, this book provides an up-to-date summary of central topics in the field of nonequilibrium statistical mechanics and dynamical systems theory. Understanding macroscopic properties of matter starting from microscopic chaos in the equations of motion of single atoms or molecules is a key problem in nonequilibrium statistical mechanics. Of particular interest both for theory and applications are transport processes such as diffusion, reaction, conduction and viscosity. Recent advances towards a deterministic theory of nonequilibrium statistical physics are summarized: Both Hamiltonian dynamical systems under nonequilibrium boundary conditions and non-Hamiltonian modelings of nonequilibrium steady states by using thermal reservoirs are considered. The surprising new results include transport coefficients that are fractal functions of control parameters, fundamental relations between transport coefficients and chaos quantities, and an understanding of nonequilibrium entropy production in terms of fractal measures and attractors. The theory is particularly useful for the description of many-particle systems with properties in-between conventional thermodynamics and nonlinear science, as they are frequently encountered on nanoscales.

"This book provides various approaches to computational gas-solids flow and will aid the researchers, graduate students and practicing engineers in this rapidly expanding area"--Provided by publisher.

Certain forms of the Boltzmann equation, have emerged, which relinquish most mathematical complexities of the true Boltzmann equation. This text provides a detailed survey of Lattice Boltzmann equation theory and its major applications.