Geometry and Topology in Hamiltonian Dynamics and Statistical Mechanics (Paperback)

Marco Pettini

ISBN 10: 1441921648 / ISBN 13: 9781441921642

Edité par Springer-Verlag New York Inc., New York, NY, 2010

Paperback. Itisaspecialpleasureformetowritethisforewordforaremarkablebookbya remarkableauthor.MarcoPettiniisadeepthinker,whohasspentmanyyears probing the foundations of Hamiltonian chaos and statistical mechanics, in particular phase transitions, from the point of view of geometry and topology. Itisinparticularthequalityofmindoftheauthorandhisdeepphysical,as well as mathematical insights which make this book so special and inspiring. It is a must for those who want to venture into a new approach to old problems or want to use new tools for new problems. Although topology has penetrated a number of ?elds of physics, a broad participationoftopologyintheclari?cationandprogressoffundamentalpr- lems in the above-mentioned ?elds has been lacking. The new perspectives topology gives to the above-mentioned problems are bound to help in their clari?cation and to spread to other ?elds of science. The sparsity of geometric thinking and of its use to solve fundamental problems, when compared with purely analytical methods in physics, could be relieved and made highly productive using the material discussed in this book. It is unavoidable that the physicist reader may have then to learn some new mathematics and be challenged to a new way of thinking, but with the author as a guide, he is assured of the best help in achieving this that is presently available. It is a must for those who want to venture into a new approach to old problems or want to use new tools for new problems. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. N° de réf. du vendeur 9781441921642

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.

À propos de l?auteur: 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.

Détails bibliographiques

Titre : Geometry and Topology in Hamiltonian ...
Éditeur : Springer-Verlag New York Inc., New York, NY
Date d'édition : 2010
Reliure : Paperback
Etat : new