Complex Hamiltonian Dynamics
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Complex Hamiltonian Dynamics
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Author : Tassos Bountis
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-04-03
Complex Hamiltonian Dynamics written by Tassos Bountis and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-03 with Language Arts & Disciplines categories.
This book explores modern developments in Hamiltonian dynamical systems, focusing on high degree-of-freedom systems and the transitional regimes between regular and chaotic motion. Includes end-of-chapter exercises and challenging problems.
Complex Hamiltonian Dynamics
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Author : Tassos Bountis
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-04-03
Complex Hamiltonian Dynamics written by Tassos Bountis and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-03 with Science categories.
This book introduces and explores modern developments in the well established field of Hamiltonian dynamical systems. It focuses on high degree-of-freedom systems and the transitional regimes between regular and chaotic motion. The role of nonlinear normal modes is highlighted and the importance of low-dimensional tori in the resolution of the famous FPU paradox is emphasized. Novel powerful numerical methods are used to study localization phenomena and distinguish order from strongly and weakly chaotic regimes. The emerging hierarchy of complex structures in such regimes gives rise to particularly long-lived patterns and phenomena called quasi-stationary states, which are explored in particular in the concrete setting of one-dimensional Hamiltonian lattices and physical applications in condensed matter systems. The self-contained and pedagogical approach is blended with a unique balance between mathematical rigor, physics insights and concrete applications. End of chapter exercises and (more demanding) research oriented problems provide many opportunities to deepen the reader’s insights into specific aspects of the subject matter. Addressing a broad audience of graduate students, theoretical physicists and applied mathematicians, this text combines the benefits of a reference work with those of a self-study guide for newcomers to the field.
Modeling And Control Of Complex Physical Systems
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Author : Vincent Duindam
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-10-15
Modeling And Control Of Complex Physical Systems written by Vincent Duindam and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-15 with Technology & Engineering categories.
Energy exchange is a major foundation of the dynamics of physical systems, and, hence, in the study of complex multi-domain systems, methodologies that explicitly describe the topology of energy exchanges are instrumental in structuring the modeling and the computation of the system's dynamics and its control. This book is the outcome of the European Project "Geoplex" (FP5 IST-2001-34166) that studied and extended such system modeling and control methodologies. This unique book starts from the basic concept of port-based modeling, and extends it to port-Hamiltonian systems. This generic paradigm is applied to various physical domains, showing its power and unifying flexibility for real multi-domain systems.
Essentials Of Hamiltonian Dynamics
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Author : John H. Lowenstein
language : en
Publisher: Cambridge University Press
Release Date : 2012-01-19
Essentials Of Hamiltonian Dynamics written by John H. Lowenstein and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-19 with Mathematics categories.
Concise and pedagogical textbook that covers all the topics necessary for a graduate-level course in dynamics based on Hamiltonian methods.
Classical And Quantum Dynamics Of Constrained Hamiltonian Systems
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Author : Heinz J. Rothe
language : en
Publisher: World Scientific
Release Date : 2010
Classical And Quantum Dynamics Of Constrained Hamiltonian Systems written by Heinz J. Rothe and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
This book is an introduction to the field of constrained Hamiltonian systems and their quantization, a topic which is of central interest to theoretical physicists who wish to obtain a deeper understanding of the quantization of gauge theories, such as describing the fundamental interactions in nature. Beginning with the early work of Dirac, the book covers the main developments in the field up to more recent topics, such as the field-antifield formalism of Batalin and Vilkovisky, including a short discussion of how gauge anomalies may be incorporated into this formalism. The book is comprehensive and well-illustrated with examples, enables graduate students to follow the literature on this subject without much problems, and to perform research in this field.
Geometry And Topology In Hamiltonian Dynamics And Statistical Mechanics
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Author : Marco Pettini
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-14
Geometry And Topology In Hamiltonian Dynamics And Statistical Mechanics written by Marco Pettini and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-14 with Mathematics categories.
Itisaspecialpleasureformetowritethisforewordforaremarkablebookbya remarkableauthor.MarcoPettiniisadeepthinker,whohasspentmanyyears probing the foundations of Hamiltonian chaos and statistical mechanics, in particular phase transitions, from the point of view of geometry and topology. Itisinparticularthequalityofmindoftheauthorandhisdeepphysical,as well as mathematical insights which make this book so special and inspiring. It is a “must” for those who want to venture into a new approach to old problems or want to use new tools for new problems. Although topology has penetrated a number of ?elds of physics, a broad participationoftopologyintheclari?cationandprogressoffundamentalpr- lems in the above-mentioned ?elds has been lacking. The new perspectives topology gives to the above-mentioned problems are bound to help in their clari?cation and to spread to other ?elds of science. The sparsity of geometric thinking and of its use to solve fundamental problems, when compared with purely analytical methods in physics, could be relieved and made highly productive using the material discussed in this book. It is unavoidable that the physicist reader may have then to learn some new mathematics and be challenged to a new way of thinking, but with the author as a guide, he is assured of the best help in achieving this that is presently available.
Lagrangian And Hamiltonian Dynamics
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Author : Peter Mann
language : en
Publisher: Oxford University Press
Release Date : 2018
Lagrangian And Hamiltonian Dynamics written by Peter Mann and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Mathematics categories.
The book introduces classical mechanics. It does so in an informal style with numerous fresh, modern and inter-disciplinary applications assuming no prior knowledge of the necessary mathematics. The book provides a comprehensive and self-contained treatment of the subject matter up to the forefront of research in multiple areas.
Notes On Hamiltonian Dynamical Systems
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Author : Antonio Giorgilli
language : en
Publisher: Cambridge University Press
Release Date : 2022-05-05
Notes On Hamiltonian Dynamical Systems written by Antonio Giorgilli and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-05 with Science categories.
Starting with the basics of Hamiltonian dynamics and canonical transformations, this text follows the historical development of the theory culminating in recent results: the Kolmogorov–Arnold–Moser theorem, Nekhoroshev's theorem and superexponential stability. Its analytic approach allows students to learn about perturbation methods leading to advanced results. Key topics covered include Liouville's theorem, the proof of Poincaré's non-integrability theorem and the nonlinear dynamics in the neighbourhood of equilibria. The theorem of Kolmogorov on persistence of invariant tori and the theory of exponential stability of Nekhoroshev are proved via constructive algorithms based on the Lie series method. A final chapter is devoted to the discovery of chaos by Poincaré and its relations with integrability, also including recent results on superexponential stability. Written in an accessible, self-contained way with few prerequisites, this book can serve as an introductory text for senior undergraduate and graduate students.
Symplectic Invariants And Hamiltonian Dynamics
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Author : Helmut Hofer
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-03-31
Symplectic Invariants And Hamiltonian Dynamics written by Helmut Hofer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-31 with Mathematics categories.
The discoveries of the last decades have opened new perspectives for the old field of Hamiltonian systems and led to the creation of a new field: symplectic topology. Surprising rigidity phenomena demonstrate that the nature of symplectic mappings is very different from that of volume preserving mappings. This raises new questions, many of them still unanswered. On the other hand, analysis of an old variational principle in classical mechanics has established global periodic phenomena in Hamiltonian systems. As it turns out, these seemingly different phenomena are mysteriously related. One of the links is a class of symplectic invariants, called symplectic capacities. These invariants are the main theme of this book, which includes such topics as basic symplectic geometry, symplectic capacities and rigidity, periodic orbits for Hamiltonian systems and the action principle, a bi-invariant metric on the symplectic diffeomorphism group and its geometry, symplectic fixed point theory, the Arnold conjectures and first order elliptic systems, and finally a survey on Floer homology and symplectic homology. The exposition is self-contained and addressed to researchers and students from the graduate level onwards.
Non Hermitian Hamiltonians In Quantum Physics
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Author : Fabio Bagarello
language : en
Publisher: Springer
Release Date : 2016-05-27
Non Hermitian Hamiltonians In Quantum Physics written by Fabio Bagarello and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-27 with Science categories.
This book presents the Proceedings of the 15th International Conference on Non-Hermitian Hamiltonians in Quantum Physics, held in Palermo, Italy, from 18 to 23 May 2015. Non-Hermitian operators, and non-Hermitian Hamiltonians in particular, have recently received considerable attention from both the mathematics and physics communities. There has been a growing interest in non-Hermitian Hamiltonians in quantum physics since the discovery that PT-symmetric Hamiltonians can have a real spectrum and thus a physical relevance. The main subjects considered in this book include: PT-symmetry in quantum physics, PT-optics, Spectral singularities and spectral techniques, Indefinite-metric theories, Open quantum systems, Krein space methods, and Biorthogonal systems and applications. The book also provides a summary of recent advances in pseudo-Hermitian Hamiltonians and PT-symmetric Hamiltonians, as well as their applications in quantum physics and in the theory of open quantum systems.