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Author: Giovanni Gallavotti
Publisher: Springer Science & Business Media
ISBN: 3662058537
Category : Mathematics
Languages : en
Pages : 439
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Book Description
Intended for beginners in ergodic theory, this introductory textbook addresses students as well as researchers in mathematical physics. The main novelty is the systematic treatment of characteristic problems in ergodic theory by a unified method in terms of convergent power series and renormalization group methods, in particular. Basic concepts of ergodicity, like Gibbs states, are developed and applied to, e.g., Asonov systems or KAM Theroy. Many examples illustrate the ideas and, in addition, a substantial number of interesting topics are treated in the form of guided problems.
Author: Giovanni Gallavotti
Publisher: Springer Science & Business Media
ISBN: 3662058537
Category : Mathematics
Languages : en
Pages : 439
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Book Description
Intended for beginners in ergodic theory, this introductory textbook addresses students as well as researchers in mathematical physics. The main novelty is the systematic treatment of characteristic problems in ergodic theory by a unified method in terms of convergent power series and renormalization group methods, in particular. Basic concepts of ergodicity, like Gibbs states, are developed and applied to, e.g., Asonov systems or KAM Theroy. Many examples illustrate the ideas and, in addition, a substantial number of interesting topics are treated in the form of guided problems.
Author: Alexander Leonidovich Kuzemsky
Publisher: World Scientific
ISBN: 9811267022
Category : Science
Languages : en
Pages : 484
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Book Description
The book focuses on the study of the temporal behavior of complex many-particle systems. The phenomenon of time and its role in the temporal evolution of complex systems is a remaining mystery. The book presents the necessity of the interdisciplinary point of view regarding on the phenomenon of time.The aim of the present study is to summarize and formulate in a concise but clear form the trends and approaches to the concept of time from a broad interdisciplinary perspective exposing tersely the complementary approaches and theories of time in the context of thermodynamics, statistical physics, cosmology, theory of information, biology and biophysics, including the problem of time and aging. Various approaches to the problem show that time is an extraordinarily interdisciplinary and multifaceted underlying notion which plays an extremely important role in various natural complex processes.
Author: Giuseppe Gaeta
Publisher: Springer Nature
ISBN: 1071626213
Category : Science
Languages : en
Pages : 601
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Book Description
This volume in the Encyclopedia of Complexity and Systems Science, Second Edition, is devoted to the fundamentals of Perturbation Theory (PT) as well as key applications areas such as Classical and Quantum Mechanics, Celestial Mechanics, and Molecular Dynamics. Less traditional fields of application, such as Biological Evolution, are also discussed. Leading scientists in each area of the field provide a comprehensive picture of the landscape and the state of the art, with the specific goal of combining mathematical rigor, explicit computational methods, and relevance to concrete applications. New to this edition are chapters on Water Waves, Rogue Waves, Multiple Scales methods, legged locomotion, Condensed Matter among others, while all other contributions have been revised and updated. Coverage includes the theory of (Poincare’-Birkhoff) Normal Forms, aspects of PT in specific mathematical settings (Hamiltonian, KAM theory, Nekhoroshev theory, and symmetric systems), technical problems arising in PT with solutions, convergence of series expansions, diagrammatic methods, parametric resonance, systems with nilpotent real part, PT for non-smooth systems, and on PT for PDEs [write out this acronym partial differential equations]. Another group of papers is focused specifically on applications to Celestial Mechanics, Quantum Mechanics and the related semiclassical PT, Quantum Bifurcations, Molecular Dynamics, the so-called choreographies in the N-body problem, as well as Evolutionary Theory. Overall, this unique volume serves to demonstrate the wide utility of PT, while creating a foundation for innovations from a new generation of graduate students and professionals in Physics, Mathematics, Mechanics, Engineering and the Biological Sciences.
Author: Howard J. Carmichael
Publisher: Springer Science & Business Media
ISBN: 3540713204
Category : Science
Languages : en
Pages : 551
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Book Description
This second volume of Howard Carmichael’s work continues the development of the methods used in quantum optics to treat open quantum systems and their fluctuations. Its early chapters build upon the phase-space methods introduced in Volume 1. Written on a level suitable for debut researchers or students in an advanced course in quantum optics, or a course in quantum mechanics or statistical physics that deals with open quantum systems.
Author: Errico Presutti
Publisher: Springer Science & Business Media
ISBN: 3540733051
Category : Mathematics
Languages : en
Pages : 478
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Book Description
Collective behavior in systems with many components, blow-ups with emergence of microstructures are proofs of the double, continuum and atomistic, nature of macroscopic systems, an issue which has always intrigued scientists and philosophers. Modern technologies have made the question more actual and concrete with recent, remarkable progresses also from a mathematical point of view. The book focuses on the links connecting statistical and continuum mechanics and, starting from elementary introductions to both theories, it leads to actual research themes. Mathematical techniques and methods from probability, calculus of variations and PDE are discussed at length.
Author: Dénes Petz
Publisher: Springer Science & Business Media
ISBN: 3540746366
Category : Science
Languages : en
Pages : 221
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Book Description
This concise and readable book addresses primarily readers with a background in classical statistical physics and introduces quantum mechanical notions as required. Conceived as a primer to bridge the gap between statistical physics and quantum information, it emphasizes concepts and thorough discussions of the fundamental notions and prepares the reader for deeper studies, not least through a selection of well chosen exercises.
Author: Jouni Suhonen
Publisher: Springer Science & Business Media
ISBN: 3540488618
Category : Science
Languages : en
Pages : 655
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Book Description
From Nucleons to Nucleus deals with single-particle and collective features of spherical nuclei. Each nuclear model is introduced and derived in detail. The formalism is then applied to light and medium-heavy nuclei in worked-out examples, and finally the acquired skills are strengthened by a wide selection of exercises, many relating the models to experimental data. Nuclear properties are discussed using particles, holes and quasi-particles. From Nucleons to Nucleus is based on lectures on nuclear physics given by the author, and serves well as a textbook for advanced students. Researchers too will appreciate it as a well-balanced reference to theoretical nuclear physics.
Author: Pierre Collet
Publisher: Springer Science & Business Media
ISBN: 3540347062
Category : Mathematics
Languages : en
Pages : 238
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Book Description
The study of dynamical systems is a well established field. This book provides a panorama of several aspects of interest to mathematicians and physicists. It collects the material of several courses at the graduate level given by the authors, avoiding detailed proofs in exchange for numerous illustrations and examples. Apart from common subjects in this field, a lot of attention is given to questions of physical measurement and stochastic properties of chaotic dynamical systems.
Author: Akihito Hora
Publisher: Springer Science & Business Media
ISBN: 3540488634
Category : Science
Languages : en
Pages : 384
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Book Description
This is the first book to comprehensively cover quantum probabilistic approaches to spectral analysis of graphs, an approach developed by the authors. The book functions as a concise introduction to quantum probability from an algebraic aspect. Here readers will learn several powerful methods and techniques of wide applicability, recently developed under the name of quantum probability. The exercises at the end of each chapter help to deepen understanding.
Author: Antonio Fasano
Publisher: OUP Oxford
ISBN: 9780191513596
Category : Mathematics
Languages : en
Pages : 788
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Book Description
Analytical Mechanics is the investigation of motion with the rigorous tools of mathematics, with remarkable applications to many branches of physics (Astronomy, Statistical and Quantum Mechanics, etc.). Rooted in the works of Lagrange, Euler, and Poincaré, it is a classical subject with fascinating developments and still rich with open problems. It addresses such fundamental questions as: Is the solar system stable? Is there a unifying "economy" principle in mechanics? How can a point mass be described as a "wave"? This book was written to fill a gap between elementary expositions and more advanced (and clearly more stimulating) material. It takes the challenge to explain the most relevant ideas and to show the most important applications using plain language and "simple" mathematics, often through an original approach. Basic calculus is enough for the reader to proceed through the book and when more is required, the new mathematical concepts are illustrated, again in plain language. The book is conceived in such a way that some difficult chapters can be bypassed, whilst still grasping the main ideas. However, anybody wishing to go deeper in some directions will find at least the flavour of recent developments and many bibliographical references. Theory is always accompanied by examples. Many problems are suggested and some are completely worked out at the end of each chapter. The book may effectively be used (and it is in several Italian Universities) for undergraduate as well as for PhD courses in Physics and Mathematics at various levels.
