From Quasicrystals to More Complex Systems

The prime objective of this book is to bring about a fundamental understanding of aperiodic solids with long range order (incommensurate phases, quasicrystals), and of glasses and more complex systems (fractal, chaotic). It provides a comprehensive insight into the most recent concepts and tools of Condensed Matter Physics. The first part of this book is devoted to methods and results on quasicrystals. Next, it deals with models and concepts currently at work in studies on aperiodic media and phenomena. The third part is devoted to glasses, and to dynamical systems as applied to condensed matter with emphasis on the most salient experimental and theoretical developments on fractal and multifractal analysis relevant to the fields. The deliberate pedagogical aim of the School also stands out in the Glossary written by the Editors, with suggestions by the Authors. It will help the readers, - particularly the experimentalists, - to find their way throughout the book.

Texte du rabat

This book is a collection of part of the written versions of the Physics Courses given at the Winter School "Order, Chance and Risk: Aperiodic Phenomena from Solid State to Finance" held at the Les Houches Center for Physics, between February 23 and March 6, 1998. The School gathered lecturers and participants from all over the world. On a thematic level, the content of the school can be viewed both as a continuation (aperiodic phenomena in solid state physics) and an extension (mathematical aspects of fmance and economy) of the previous "Beyond Quasicrystals", also held at Les Houches, March 7-18 1994 and published in the same ·series. One of its important goals was to promote in-depth concrete scientific exchanges between theoretical physicists, experimental physicists and mathematicians on the one hand, and on the other hand practitioners of the economico-fmancial sphere and specialists of financial mathematics. Therefore, besides the mathematical tools and concepts at work in theoretical descriptions, relevant experimental data were also presented together with methods allowing their interpretation. As a result of this choice, the School was stimulated by experimentalists and fmancial market operators who joined the theoretical physicists and mathematicians at the conference. The present volume deals with the theoretical and experimental studies on aperiodic solids with long range order, incommensurate phases, quasicrystals, glasses, and more complex systems (fractal, chaotic), while a second volume to appear in the same series is devoted to the finance and economy facet.

Contenu

Course 1 Dynamics and Transport Properties of Aperiodic Crystals.- Course 2 Diffraction Experiments on Quasicrystals and Related Phases.- Course 3 Electronic Properties of Quasicrystals. A Comparison with Approximant Phases and Disordered Systems.- Course 4 Exact Electron States in 1D (Quasi-) Periodic Arrays of Delta-Potentials.- Course 5 Random Tiling Models for Quasicrystals.- Course 6 Model Sets: A Survey.- Course 7 Acceptance Windows Compatible with a Quasicrystal Fragment.- Course 8 Counting Systems with Irrational Basis for Quasicrystals.- Course 9 Acoustic-Like Excitations in Strongly Disordered Media.- Course 10 Intermittent Dynamics and Ageing in Glassy Systems.- Course 11 A Short Introduction to Ergodic Theory and Its Applications.- Course 12 Fractality and the Kinetics of Chaos.- Course 13 Long-Tailed Distributions in Physics.- Course 14 Distribution of Galaxies: Scaling vs. Fractality.