Products of Random Matrices

in Statistical Physics

Andrea Crisanti, Giovanni Paladin, Angelo Vulpiani (Autoren)

Buch | Softcover

XIV, 169 Seiten

2012 | 1. Softcover reprint of the original 1st ed. 1993
Springer Berlin (Verlag)
978-3-642-84944-2 (ISBN)

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At the present moment, after the success of the renormalization group in providing a conceptual framework for studying second-order phase tran sitions, we have a nearly satisfactory understanding of the statistical me 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 ma 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.

Products of random matrices arise naturally in many areas of condensed-matter and statistical physics. This book provides a self-contained introduction, suitable for graduate students and researchers, to such products and to methods for the calculation of the corresponding Lyapunov exponents.

I Background.- 1. Why Study Random Matrices?.- 2. Lyapunov Exponents for PRM.- II Applications.- 3. Chaotic Dynamical Systems.- 4. Disordered Systems.- 5. Localization.- III Miscellany.- 6. Other Applications.- 7. Appendices.- References.

Erscheint lt. Verlag	5.1.2012
Reihe/Serie	Springer Series in Solid-State Sciences
Zusatzinfo	XIV, 169 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	294 g
Themenwelt	Naturwissenschaften ► Physik / Astronomie ► Thermodynamik
Schlagworte	Chaotic Systems • Deterministic Chaos • disordered system • Disordered Systems • Dynamical Systems • Fields • Lyapunov exponents • Mechanics • numerical method • Physics • Products of random matrices • Random Media • Statistical Mechanics • Statistical Physics • Wave
ISBN-10	3-642-84944-X / 364284944X
ISBN-13	978-3-642-84944-2 / 9783642849442
Zustand	Neuware