Fractals, Quasicrystals, Chaos, Knots and Algebraic Quantum Mechanics

1. Front Matter

   Pages i-xiv

   PDF

2. Fractal Patterns in Chemistry

   • G. Zumofen, A. Blumen, J. Klafter

   Pages 1-20

3. Fractal Concepts in Reaction Kinetics

   • A. Blumen, G. Zumofen, J. Klafter

   Pages 21-52

4. Fractal Character of Chemical Reactions in Disordered Media

   • Panos Argyrakis

   Pages 53-64

5. Reaction Kinetics for Diffusion Controlled Aggregation

   • F. Leyvraz

   Pages 65-72

6. Quasicrystals: From Periodic to Non-Periodic Order in Solids

   • Peter Kramer

   Pages 73-91

7. Crystallography of Quasicrystals

   • A. Janner

   Pages 93-109

8. N-dimensional crystallographic description of the icosahedral phases; the example of the Al73Mn21Si6 quasiperiodic structure

   • D. Gratias, J. W. Cahn, M. Bessiere, Y. Calvayrac, S. Lefebvre, A. Quivy et al.

   Pages 111-119

9. The Growth of Icosahedral Phase

   • Veit Elser

   Pages 121-138

10. On the Electronic Structure of Calaverite

    • B. Krutzen

    Pages 139-141

11. Chaotic Behavior of Classical Hamiltonian Systems

    • H.-D. Meyer

    Pages 143-157

12. Statistical Properties of Energy Levels and Connection to Classical Mechanics

    • L. S. Cederbaum, Th. Zimmermann, H. Köppel, H.-D. Meyer

    Pages 159-173

13. Quantum Suppression of Classical Chaos and Microwave Ionization of Hydrogen Atom

    • Giulio Casati

    Pages 175-187

14. Quantum Limitation of Chaotic Diffusion and Underthreshold Ionization

    • Italo Guarneri

    Pages 189-194

15. A Ro-Vibrational Study of Regular/Irregular Behaviour of the CO-Ar System

    • Stavros C. Farantos, Jonathan Tennyson

    Pages 195-206

16. Analysis of DNA knots and catenanes allows to deduce the mechanism of action of enzymes which cut and join DNA strands

    • Andrzej Stasiak, Theodor Koller

    Pages 207-219

17. Using Knot Theory to Analyze DNA Experiments

    • D. W. Sumners

    Pages 221-232

18. Introduction to Knot and Link Polynomials

    • P. de la Harpe

    Pages 233-263

19. Long Range Dynamics and Spontaneous Symmetry Breaking in Many-Body Systems

    • F. Strocchi

    Pages 265-285

20. Theoretical Concepts in Quantum Probability; Quantum Markov Processes

    • Hans Maassen

    Pages 287-302

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.

• DNA
• chaos
• chemical reaction
• chemistry
• crystallography
• enzymes
• kinetics
• physical chemistry
• quantum mechanics
• quantum physics
• structure

`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.

• Laboratory of Physical Chemistry, ETH-Zentrum, Zürich, Switzerland

  A. Amann

• Physical Chemistry Institute, University of Heidelberg, Heidelberg, Germany

  L. S. Cederbaum

• Institute of Physical Chemistry, Institut für Quantenchemie, Freie Universitat Berlin, Berlin 45, Germany

  W. Gans

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