Fractals, Quasicrystals, Chaos, Knots and Algebraic Quantum Mechanics

At the end of the workshop on "New Theoretical Concepts in Physical Chemistry", one of the participants made an attempt to present a first impression of its achievements from his own personal standpoint. Appar ently his views reflected a general feeling, so that the organizers thought they would be suitable as a presentation of the proceedings for future readers. That is the background from which this foreword was born. The scope of the workshop is a very broad one. There are contribu tions from mathematics, physics, crystallography, chemistry and biology; the problems are approached either by means of axiomatic and rigorous methods, or at an empirical phenomenological level. This same diversifi cation can be found in the new basic concepts presented. Some arise from pure theoretical investigation in C*-algebra or in quantum probability theory; others from an analysis of very complex experimental data like nuclear energy levels, or processes on the frontier between classical and quantum physics; others again have their origin in the discovery of new ordered structures like the icosahedral crystal phases, or the knots of DNA molecules; others follow from the application of ideas like frac tals or chaos to new fields like spectral theory or chemical reactions. It is to be expected that readers will have to face the same sort of difficulties as did the participants in understanding such diverse languages, in applying themselves to subjects possibly far from their own experience, and in grasping highly sophisticated new concepts.

Autorentext
Anton Amann ist emeritierter Universitätsprofessor für Soziologie und Sozialgerontologie am Institut für Soziologie der Universität Wien und Wissenschaftlicher Leiter des "Zentrums für Alternswissenschaften, Gesundheits- und Sozialpolitikforschung" (ZENTAS) an der Niederösterreichischen Landesakademie.

Klappentext

Proceedings of the NATO Advanced Research Workshop, Acquafredda di Maratea, Italy, October 4-8, 1987

Zusammenfassung
`The present book might be appealing to theoretical chemists because the interesting mixture of mathematics, physics and chemistry is rather stimulating and it presents problems, concepts andd results which do not belong to the standard knowledge of theoretical chemists yet.'
T. Hoffmann-Odrmhof and P. Schuster, Theoretica Chimica Acta, Vol. 76, 1989.

Inhalt
Fractal Patterns in Chemistry.- Fractal Concepts in Reaction Kinetics.- Fractal Character of Chemical Reactions in Disordered Media.- Reaction Kinetics for Diffusion Controlled Aggregation.- Quasicrystals: From Periodic to Non-Periodic order in Solids.- Crystallography of Quasicrystals.- N-Dimensional Crystallographic Description of Icosahedral Phases; The Example of the Al73Mn21Si6 Quasiperiodic Structure.- The Growth of Icosahedral Phase.- On the Electronic Structure of Calaverite.- Chaotic Behavior of Classical Hamiltonian Systems.- Statistical Properties of Energy Levels and Connection to Classical Mechanics.- Quantum Suppression of Classical Chaos and Microwave Ionization of Hydrogen Atom.- Quantum Limitation of Chaotic Diffusion and Under-Threshold Ionization.- A Ro-Vibrational Study for the Regular/irregular Behaviour of the Co-Ar System.- Analysis of DNA Knots and Catenanes Allows to Deduce the Mechanism of Action of Enzymes Which Cut and Join DNA Strands.- Using Knot Theory to Analyze DNA Experiments.- to Knot and Link Polynomials.- Long Range Dynamics and Spontaneous Symmetry Breaking in Many-Body Systems.- Theoretical Concepts in Quantum Probability; Quantum Markov Processes.- The Large Deviation Principle in Statistical Mechanics.- Chirality as a Classical Observable in Algebraic Quantum Mechanics.