Geometry and Topology in Hamiltonian Dynamics and Statistical Mechanics
Pettini, Marco
ISBN 10: 1441921648 ISBN 13: 9781441921642
Published by Springer, 2010
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Soft cover
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Synopsis:
This book covers a new explanation of the origin of Hamiltonian chaos and its quantitative characterization. The subject of the book is very original and nothing similar has been written hitherto. There are numerous illustrations throughout and the book will be of interest to both mathematicians and physicists. The author focuses on two main areas: Riemannian formulation of Hamiltonian dynamics, providing an original viewpoint about the relationship between geodesic instability and curvature properties of the mechanical manifolds; and a topological theory of thermodynamic phase transitions, relating topology changes of microscopic configuration space with the generation of singularities of thermodynamic observables. The two areas are strongly related because the geometrization of microscopic dynamics, which is the ultimate physical source of phase transitions, naturally leads to investigate how geometry and topology of the mechanical manifolds have to change to induce a phase transition.
About the Author: The author is one of few pioneering individuals in this recently emerged important research area. His book will be a unique contribution to the field.
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Bibliographic Details
Title: Geometry and Topology in Hamiltonian ...
Publisher: Springer
Publication Date: 2010
Binding: Soft cover
Condition: New