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| Author | : FRITZ |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 489 |
| Release | : 2013-11-22 |
| Genre | : Science |
| ISBN | : 1489966536 |
| Author | : I͡Akov Grigorʹevich Sinaĭ |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 266 |
| Release | : 1991 |
| Genre | : Mathematics |
| ISBN | : 9780821841020 |
Dynamical systems and statistical mechanics have been developing in close interaction during the past decade, and the papers in this book attest to the productiveness of this interaction. The first paper in the collection contains a new result in the theory of quantum chaos, a burgeoning line of inquiry which combines mathematics and physics and which is likely in time to produce many new connections and applications. Another paper, related to the renormalization group method for the study of maps of the circle with singularities due to a jump in the derivative, demonstrates that the fixed point of the renormgroup can in this case be sufficiently described. In certain situations, the renormgroup methods work better than the traditional KAM method. Other topics covered include: thermodynamic formalism for certain infinite-dimensional dynamical systems, numerical simulation of dynamical systems with hyperbolic behaviour, periodic points of holomorphic maps, the theory of random media, statistical properties of the leading eigenvalue in matrix ensembles of large dimension, spectral properties of the one-dimensional Schrodinger operator. This volume will appeal to many readers, as it covers a broad range of topics and presents a view of some of the frontier research in the Soviet Union today.
| Author | : J. Fritz |
| Publisher | : |
| Total Pages | : 508 |
| Release | : 2014-09-01 |
| Genre | : |
| ISBN | : 9781489966544 |
| Author | : FRITZ |
| Publisher | : Birkhäuser |
| Total Pages | : 0 |
| Release | : 1985-01-01 |
| Genre | : Science |
| ISBN | : 9780817633004 |
"Contains most of the invited papers of the Second Colloquium and Workshop on 'Random Fields: Rigorous Results in Statistical Mechanics' held in K'oszeg, Hungary between August 26 and September 1, 1984"--Pref.
| Author | : Nikolaĭ Nikolaevich Bogoli͡ubov |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 260 |
| Release | : 1992 |
| Genre | : Mathematics |
| ISBN | : 9780821831441 |
This volume contains articles covering a wide range of current directions in modern statistical mechanics and dynamical systems theory. Scientists, researchers, and students working in mathematical physics and statistical mechanics will find this book of great interest. Among the topics covered are: phase transition problems, including superconductivity and superfluidity; methods of nonequilibrium statistical mechanics and fluctuation theory; quantum collective phenomena; superradiance; spin glasses; polaron problems; chains of Bogolyubov equations and kinetic equations; algebraic aspects of quantum-dynamical semigroups; the collective variables method; and qualitative properties of classical dynamical systems."
| Author | : Shamik Gupta |
| Publisher | : Springer |
| Total Pages | : 121 |
| Release | : 2018-08-28 |
| Genre | : Science |
| ISBN | : 3319966642 |
This book introduces and discusses the analysis of interacting many-body complex systems exhibiting spontaneous synchronization from the perspective of nonequilibrium statistical physics. While such systems have been mostly studied using dynamical system theory, the book underlines the usefulness of the statistical physics approach to obtain insightful results in a number of representative dynamical settings. Although it is intractable to follow the dynamics of a particular initial condition, statistical physics allows to derive exact analytical results in the limit of an infinite number of interacting units. Chapter one discusses dynamical characterization of individual units of synchronizing systems as well as of their interaction and summarizes the relevant tools of statistical physics. The latter are then used in chapters two and three to discuss respectively synchronizing systems with either a first- or a second-order evolution in time. This book provides a timely introduction to the subject and is meant for the uninitiated as well as for experienced researchers working in areas of nonlinear dynamics and chaos, statistical physics, and complex systems.
| Author | : Eric Bertin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 85 |
| Release | : 2011-09-28 |
| Genre | : Science |
| ISBN | : 3642239234 |
This concise primer (based on lectures given at summer schools on complex systems and on a masters degree course in complex systems modeling) will provide graduate students and newcomers to the field with the basic knowledge of the concepts and methods of statistical physics and its potential for application to interdisciplinary topics. Indeed, in recent years, statistical physics has begun to attract the interest of a broad community of researchers in the field of complex system sciences, ranging from biology to the social sciences, economics and computer science. More generally, a growing number of graduate students and researchers feel the need to learn some basic concepts and questions originating in other disciplines without necessarily having to master all of the corresponding technicalities and jargon. Generally speaking, the goals of statistical physics may be summarized as follows: on the one hand to study systems composed of a large number of interacting ‘entities’, and on the other to predict the macroscopic (or collective) behavior of the system considered from the microscopic laws ruling the dynamics of the individual ‘entities’. These two goals are, to some extent, also shared by what is nowadays called ‘complex systems science’ and for these reasons, systems studied in the framework of statistical physics may be considered as among the simplest examples of complex systems—allowing in addition a rather well developed mathematical treatment.
| Author | : Gregoire Nicolis |
| Publisher | : World Scientific |
| Total Pages | : 343 |
| Release | : 2007 |
| Genre | : Science |
| ISBN | : 981277565X |
A geometric process is a simple monotone process that was first introduced by the author in 1988. It is a generalization of renewal process. This book captures the extensive research work on geometric processes that has been done since then in both probability and statistics theory and various applications. Some results are published for the first time. A reference book for researchers and a handbook for practioners, it is also a useful textbook for postgraduate or senior undergraduate students.
| Author | : Gza Gyrgyi |
| Publisher | : World Scientific |
| Total Pages | : 608 |
| Release | : 1992 |
| Genre | : Science |
| ISBN | : 9789810209384 |
This volume comprises about forty research papers and essays covering a wide range of subjects in the forefront of contemporary statistical physics. The contributors are renown scientists and leading authorities in several different fields. This book is dedicated to Pter Szpfalusy on the occasion of his sixtieth birthday. Emphasis is placed on his two main areas of research, namely phase transitions and chaotic dynamical systems, as they share common aspects like the applicability of the probabilistic approach or scaling behaviour and universality. Several papers deal with equilibrium phase transitions, critical dynamics, and pattern formation. Also represented are disordered systems, random field systems, growth processes, and neural network. Statistical properties of interacting electron gases, such as the Kondo lattice, the Wigner crystal, and the Hubbard model, are treated. In the field of chaos, Hamiltonian transport and resonances, strange attractors, multifractal characteristics of chaos, and the effect of weak perturbations are discussed. A separate section is devoted to selected mathematical aspects of dynamical systems like the foundation of statistical mechanics, including the problem of ergodicity, and rigorous results on quantum chaos.
| Author | : Josef Honerkamp |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 519 |
| Release | : 2013-03-09 |
| Genre | : Science |
| ISBN | : 3662047632 |
The book is divided into two parts. The first part looks at the modeling of statistical systems before moving on to an analysis of these systems. This second edition contains new material on: estimators based on a probability distribution for the parameters; identification of stochastic models from observations; and statistical tests and classification methods.
