Chaos, Scattering and Statistical Mechanics

Pierre Gaspard

doi:10.1017/CBO9780511628856

This book describes advances in the application of chaos theory to classical scattering and nonequilibrium statistical mechanics generally, and to transport by deterministic diffusion in particular. The author presents the basic tools of dynamical systems theory, such as dynamical instability, topological analysis, periodic-orbit methods, Liouvillian dynamics, dynamical randomness and large-deviation formalism. These tools are applied to chaotic scattering and to transport in systems near equilibrium and maintained out of equilibrium. Chaotic Scattering is illustrated with disk scatterers and with examples of unimolecular chemical reactions and then generalized to transport in spatially extended systems. This book will be bought by researchers interested in chaos, dynamical systems, chaotic scattering, and statistical mechanics in theoretical, computational and mathematical physics and also in theoretical chemistry.

"...gives both the background and an overview of recent developments in nonequilibrium statistical mechanics, to which the author himself has made major contributions...an important reference book as well as an ideal tool for advanced students in the expanding and important field of statistical physics." Physics Today

"The book is nicely written...allows one to see some topics in dynamical systems with new eyes." Mathematical Reviews

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Chaos, Scattering and Statistical Mechanics

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Contents

Frontmatter
pp i-vi

Contents
pp vii-xvi

Preface
pp xvii-xx

Introduction
pp 1-11

Chapter 1 - Dynamical systems and their linear stability
pp 12-42

Chapter 2 - Topological chaos
pp 43-66

Chapter 3 - Liouvillian dynamics
pp 67-125

Chapter 4 - Probabilistic chaos
pp 126-170

Chapter 5 - Chaotic scattering
pp 171-223

Chapter 6 - Scattering theory of transport
pp 224-274

Chapter 7 - Hydrodynamic modes of diffusion
pp 275-342

Chapter 8 - Systems maintained out of equilibrium
pp 343-386

Chapter 9 - Noises as microscopic chaos
pp 387-432

Chapter 10 - Conclusions and perspectives
pp 433-457

References
pp 458-470

Index
pp 471-475

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