Quantum Mechanics In Nonlinear Systems

Author : Xiao-Feng Pang
Publisher : World Scientific
ISBN 13 : 9812561161
Total Pages : 646 pages
Book Rating : 4.69/5 ( download)

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Download or read book Quantum Mechanics in Nonlinear Systems written by Xiao-Feng Pang and published by World Scientific. This book was released on 2005 with total page 646 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the history of physics and science, quantum mechanics has served as the foundation of modern science. This book discusses the properties of microscopic particles in nonlinear systems, principles of the nonlinear quantum mechanical theory, and its applications in condensed matter, polymers and biological systems.The book is essentially composed of three parts. The first part presents a review of linear quantum mechanics, as well as theoretical and experimental fundamentals that establish the nonlinear quantum mechanical theory. The theory itself and its essential features are covered in the second part. In the final part, extensive applications of this theory in physics, biology and polymer are introduced. The whole volume forms a complete system of nonlinear quantum mechanics.The book is intended for researchers, graduate students as well as upper-level undergraduates.

Author : Philip Barnes Burt
Publisher : CRC Press
ISBN 13 : 9783718600724
Total Pages : 352 pages
Book Rating : 4.22/5 ( download)

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Download or read book Quantum Mechanics and Nonlinear Waves written by Philip Barnes Burt and published by CRC Press. This book was released on 1981 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Dieter Schuch
Publisher : Springer
ISBN 13 : 3319655949
Total Pages : 258 pages
Book Rating : 4.49/5 ( download)

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Download or read book Quantum Theory from a Nonlinear Perspective written by Dieter Schuch and published by Springer. This book was released on 2018-01-20 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a unique survey displaying the power of Riccati equations to describe reversible and irreversible processes in physics and, in particular, quantum physics. Quantum mechanics is supposedly linear, invariant under time-reversal, conserving energy and, in contrast to classical theories, essentially based on the use of complex quantities. However, on a macroscopic level, processes apparently obey nonlinear irreversible evolution equations and dissipate energy. The Riccati equation, a nonlinear equation that can be linearized, has the potential to link these two worlds when applied to complex quantities. The nonlinearity can provide information about the phase-amplitude correlations of the complex quantities that cannot be obtained from the linearized form. As revealed in this wide ranging treatment, Riccati equations can also be found in many diverse fields of physics from Bose-Einstein-condensates to cosmology. The book will appeal to graduate students and theoretical physicists interested in a consistent mathematical description of physical laws.

Author : Sandro Wimberger
Publisher : Springer
ISBN 13 : 331906343X
Total Pages : 215 pages
Book Rating : 4.30/5 ( download)

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Download or read book Nonlinear Dynamics and Quantum Chaos written by Sandro Wimberger and published by Springer. This book was released on 2014-05-13 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of nonlinear dynamics and chaos has grown very much over the last few decades and is becoming more and more relevant in different disciplines. This book presents a clear and concise introduction to the field of nonlinear dynamics and chaos, suitable for graduate students in mathematics, physics, chemistry, engineering, and in natural sciences in general. It provides a thorough and modern introduction to the concepts of Hamiltonian dynamical systems' theory combining in a comprehensive way classical and quantum mechanical description. It covers a wide range of topics usually not found in similar books. Motivations of the respective subjects and a clear presentation eases the understanding. The book is based on lectures on classical and quantum chaos held by the author at Heidelberg University. It contains exercises and worked examples, which makes it ideal for an introductory course for students as well as for researchers starting to work in the field.

Author : Vasily Tarasov
Publisher : Elsevier
ISBN 13 : 9780080559711
Total Pages : 530 pages
Book Rating : 4.19/5 ( download)

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Download or read book Quantum Mechanics of Non-Hamiltonian and Dissipative Systems written by Vasily Tarasov and published by Elsevier. This book was released on 2008-06-06 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum Mechanics of Non-Hamiltonian and Dissipative Systems is self-contained and can be used by students without a previous course in modern mathematics and physics. The book describes the modern structure of the theory, and covers the fundamental results of last 15 years. The book has been recommended by Russian Ministry of Education as the textbook for graduate students and has been used for graduate student lectures from 1998 to 2006. • Requires no preliminary knowledge of graduate and advanced mathematics • Discusses the fundamental results of last 15 years in this theory • Suitable for courses for undergraduate students as well as graduate students and specialists in physics mathematics and other sciences

Author : Peter D. Drummond
Publisher : Cambridge University Press
ISBN 13 : 1107004217
Total Pages : 385 pages
Book Rating : 4.14/5 ( download)

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Download or read book The Quantum Theory of Nonlinear Optics written by Peter D. Drummond and published by Cambridge University Press. This book was released on 2014-03-27 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained treatment of field quantization requires no prior knowledge of nonlinear optics. Supplemented by end-of-chapter exercises and detailed examples of calculation techniques in different systems, it is a valuable resource for graduate students and researchers in nonlinear optics, condensed matter physics, quantum information and atomic physics.

Author : Xiao-Feng Pang
Publisher : Nova Science Publishers
ISBN 13 : 9781611220117
Total Pages : 0 pages
Book Rating : 4.14/5 ( download)

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Download or read book Nonlinear Quantum Mechanics and Its Applications written by Xiao-Feng Pang and published by Nova Science Publishers. This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes complete nonlinear quantum mechanics, in which the fundamental and necessity theoretical principle and wave-corpuscle duality of microscopic particles were the foundation of this principle and its experimental evidences, the mechanisms of generation of the nonlinear interactions and its effects, as well as the methods solving nonlinear quantum mechanical problems, its distinctions with linear quantum mechanics and early nonlinear quantum mechanical idea and models, the completeness and correctness and universality of new theory as well as its applications in different systems containing polymers, physical and biological systems, which are exhibited in this book. Plenty of interesting results of these systems and a large number of novel properties of microscopic particles including the electron, proton, phonon, photon, exciton, polaron, magnon and Boson involving their localisations and classical features are stated in detail. This book is intended for researchers, teachers, graduate students, and upper level undergraduate students.

Author : Panayotis G. Kevrekidis
Publisher : Springer Nature
ISBN 13 : 3030449920
Total Pages : 389 pages
Book Rating : 4.26/5 ( download)

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Download or read book Emerging Frontiers in Nonlinear Science written by Panayotis G. Kevrekidis and published by Springer Nature. This book was released on 2020-05-29 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the impact of nonlinearity on a broad range of areas, including time-honored fields such as biology, geometry, and topology, but also modern ones such as quantum mechanics, networks, metamaterials and artificial intelligence. The concept of nonlinearity is a universal feature in mathematics, physics, chemistry and biology, and is used to characterize systems whose behavior does not amount to a superposition of simple building blocks, but rather features complex and often chaotic patterns and phenomena. Each chapter of the book features a synopsis that not only recaps the recent progress in each field but also charts the challenges that lie ahead. This interdisciplinary book presents contributions from a diverse group of experts from various fields to provide an overview of each field’s past, present and future. It will appeal to both beginners and seasoned researchers in nonlinear science, numerous areas of physics (optics, quantum physics, biophysics), and applied mathematics (ODEs, PDEs, dynamical systems, machine learning) as well as engineering.

Author : Krzysztof Kowalski
Publisher : World Scientific
ISBN 13 : 9789810217532
Total Pages : 148 pages
Book Rating : 4.36/5 ( download)

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Download or read book Methods of Hilbert Spaces in the Theory of Nonlinear Dynamical Systems written by Krzysztof Kowalski and published by World Scientific. This book was released on 1994 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first monograph on a new powerful method discovered by the author for the study of nonlinear dynamical systems relying on reduction of nonlinear differential equations to the linear abstract Schr”dinger-like equation in Hilbert space. Besides the possibility of unification of many apparently completely different techniques, the ?quantal? Hilbert space formalism introduced enables new original methods to be discovered for solving nonlinear problems arising in investigation of ordinary and partial differential equations as well as difference equations. Applications covered in the book include symmetries and first integrals, linearization transformations, B„cklund transformations, stroboscopic maps, functional equations involving the case of Feigenbaum-Cvitanovic renormalization equations and chaos.

Author : Eckehard Schöll
Publisher : Springer
ISBN 13 : 3319280287
Total Pages : 475 pages
Book Rating : 4.88/5 ( download)

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Download or read book Control of Self-Organizing Nonlinear Systems written by Eckehard Schöll and published by Springer. This book was released on 2016-01-22 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book summarizes the state-of-the-art of research on control of self-organizing nonlinear systems with contributions from leading international experts in the field. The first focus concerns recent methodological developments including control of networks and of noisy and time-delayed systems. As a second focus, the book features emerging concepts of application including control of quantum systems, soft condensed matter, and biological systems. Special topics reflecting the active research in the field are the analysis and control of chimera states in classical networks and in quantum systems, the mathematical treatment of multiscale systems, the control of colloidal and quantum transport, the control of epidemics and of neural network dynamics.