β Scribed by Dr. Andrea Crisanti, Professor Dr. Giovanni Paladin, Professor Dr. Angelo Vulpiani (auth.)
No coin nor oath required. For personal study only.
At the present moment, after the success of the renormalization group in providing a conceptual framework for studying second-order phase tranΒ sitions, we have a nearly satisfactory understanding of the statistical meΒ chanics of classical systems with a non-random Hamiltonian. The situation is completely different if we consider the theory of systems with a random Hamiltonian or of chaotic dynamical systems. The two fields are connected; in fact, in the latter the effects of deterministic chaos can be modelled by an appropriate stochastic process. Although many interesting results have been obtained in recent years and much progress has been made, we still lack a satisfactory understanding of the extremely wide variety of phenomena which are present in these fields. The study of disordered or chaotic systems is the new frontier where new ideas and techniques are being developed. More interesting and deep results are expected to come in future years. The properties of random matrices and their products form a basic tool, whose importance cannot be underestimated. They playa role as important as Fourier transforms for differential equations. This book is extremely interesting as far as it presents a unified approach for the main results which have been obtained in the study of random maΒ trices. It will become a reference book for people working in the subject. The book is written by physicists, uses the language of physics and I am sure that many physicists will read it with great pleasure.
Front Matter....Pages I-XIII
Front Matter....Pages 1-1
Why Study Random Matrices?....Pages 3-15
Lyapunov Exponents for PRM....Pages 17-40
Front Matter....Pages 41-41
Chaotic Dynamical Systems....Pages 43-58
Disordered Systems....Pages 59-85
Localization....Pages 87-113
Front Matter....Pages 115-115
Other Applications....Pages 117-133
Appendices....Pages 135-156
Back Matter....Pages 157-169
Thermodynamics; Statistical Physics, Dynamical Systems and Complexity; Condensed Matter Physics
π SIMILAR VOLUMES
This book is devoted to the theory and applications of products of random matrices, which arise naturally in many different fields. It describes analytic and numerical methods for the calculation of the corresponding Lyapunov exponents, which can be used as a tool for the analysis of problems in, fo
Random matrices are widely and successfully used in physics for almost 60-70 years, beginning with the works of Dyson and Wigner. Although it is an old subject, it is constantly developing into new areas of physics and mathematics. It constitutes now a part of the general culture of a theoretical ph
Book by Carmeli, Moshe