Geometry and Topology in Hamiltonian Dynamics and Statistical Mechanics

33, Interdisciplinary Applied Mathematics
 Buch
Sofort lieferbar
 
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.
Background in Physics.- Geometrization of Hamiltonian Dynamics.- Integrability.- Geometry and Chaos.- Geometry of Chaos and Phase Transitions.- Topological Hypothesis on the Origin.- Geometry, Topology and Thermodynamics.- Phase Transitions and Topology: Necessity Theorems.- Phase Transitions and Topology: Exact Results.- Future Developments.
This book covers a new explanation of the origin of Hamiltonian chaos and its quantitative characterization. The author focuses on two mainareas: Reimannian formulations of dynamics using either the Jacobi metric or the Eisenhart metric in extended configuration space; and topological aspects of phase transitions. Other items such as quantumsystems are also discussed in this framework. Mathematicians and physicists working in this area will find this book of interest.
Autor: Marco Pettini
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.
Autor: Marco Pettini
ISBN-13:: 9780387308920
ISBN: 038730892X
Erscheinungsjahr: 28.08.2007
Verlag: Springer-Verlag GmbH
Gewicht: 784g
Seiten: 456
Sprache: Englisch
Sonstiges: Buch, 244x162x24 mm