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Concisely and clearly written, this book provides a self-contained introduction to the basic concepts of fractals and demonstrates their use in a range of topics in condensed matter physics and statistical mechanics. The first part outlines different fractal structures observed in condensed matter. The main part of the book is dedicated to the dynamical behaviour of fractal structures, including anomalous and percolating systems. The concept of multifractals is illustrated for the metal-insulator quantum phase transition. The authors emphasize the unified description of these different dynamic problems, thus making the book accessible to readers who are new to the field.
List of contents
1. Introduction.- 2. Fractals.- 3. Percolating Networks as Random Fractals.- 4. Multifractals.- 5. Anomalous Diffusion on Fractal Networks.- 6. Atomic Vibrations of Percolating Networks.- 7. Scaling Arguments for Dynamic Structure Factors.- 8. Spin Waves in Diluted Heisenberg Antiferromagnets.- 9. Anderson Transition.- 10. Multifractals in the Anderson Transition.- Appendices.- A. Multifractality of the HRN Model.- B. Spectral Dimensions for Deterministic Fractals.- B.1 Sierpinski Gasket.- B.2 Mandelbrot-Given Fractal.- C. Diffusion and Dynamics on Networks.- C.1 Atomic Vibrations.- C.2 Spin Waves in Diluted Ferro- and Antiferromagnets.- C.3 Superconducting Networks.- D. Wigner Distributions.- References.
Summary
Concisely and clearly written, this book provides a self-contained introduction to the basic concepts of fractals and demonstrates their use in a range of topics in condensed matter physics and statistical mechanics. The first part outlines different fractal structures observed in condensed matter. The main part of the book is dedicated to the dynamical behaviour of fractal structures, including anomalous and percolating systems. The concept of multifractals is illustrated for the metal-insulator quantum phase transition. The authors emphasize the unified description of these different dynamic problems, thus making the book accessible to readers who are new to the field.
Additional text
From the reviews:
"The book provides a complete view of the fractals structures in condensed matter. Each chapter has got clear and advanced theory about the subject, gives many applications on various domains and … gives numerical simulation and experiment process. … This book could be used by those who want very advanced introduction on fractal theory and the others who research a performant work tool on the subject." (Olivier Vanoverschelde, Physicalia, Vol. 57 (3), 2005)
"The presentation is pedagogical and it starts off from elementary considerations. … To my mind the most exciting feature of the book is the treatment of the so-called Anderson transition. … I find this book both timely and inspiring. It is well written, its arguments are clearly presented and it covers areas of physics where significant progress has taken place over the last decades. I can recommend it both to students of condensed matter and experienced researchers who want an orientation in this timely area." (Professor S. Stenholm, Contemporary Physics, Vol. 45 (4), 2004)
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From the reviews:
"The book provides a complete view of the fractals structures in condensed matter. Each chapter has got clear and advanced theory about the subject, gives many applications on various domains and ... gives numerical simulation and experiment process. ... This book could be used by those who want very advanced introduction on fractal theory and the others who research a performant work tool on the subject." (Olivier Vanoverschelde, Physicalia, Vol. 57 (3), 2005)
"The presentation is pedagogical and it starts off from elementary considerations. ... To my mind the most exciting feature of the book is the treatment of the so-called Anderson transition. ... I find this book both timely and inspiring. It is well written, its arguments are clearly presented and it covers areas of physics where significant progress has taken place over the last decades. I can recommend it both to students of condensed matter and experienced researchers who want an orientation in this timely area." (Professor S. Stenholm, Contemporary Physics, Vol. 45 (4), 2004)
