Geometry and Topology in Hamiltonian Dynamics and Statistical Mechanics

Softcover version of original hardcover Auflage 2007
ISBN: 978-1-4419-2164-2
Verlag: Springer

Buch, Englisch, 453 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 709 g

Reihe: Interdisciplinary Applied Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Pettini, Marco

Fachgebiete

• Mathematik | Informatik Mathematik Topologie
• Mathematik | Informatik Mathematik Geometrie
• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

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.

Über Autor(innen)

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.