Quantum Mechanics In Nonlinear Systems

Author : Xiao-Feng Pang,Yuan-Ping Feng
Publisher : World Scientific
Page : 646 pages
File Size : 53,5 Mb
Release : 2005
Category : Science
ISBN : 9789812561169

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Quantum Mechanics in Nonlinear Systems by Xiao-Feng Pang,Yuan-Ping Feng Pdf

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
Page : 352 pages
File Size : 42,9 Mb
Release : 1981
Category : Science
ISBN : 3718600722

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Quantum Mechanics and Nonlinear Waves by Philip Barnes Burt Pdf

Author : Dieter Schuch
Publisher : Springer
Page : 258 pages
File Size : 42,9 Mb
Release : 2018-01-20
Category : Science
ISBN : 9783319655949

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Quantum Theory from a Nonlinear Perspective by Dieter Schuch Pdf

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 : Xiao-Feng Pang
Publisher : Nova Science Publishers
Page : 0 pages
File Size : 45,5 Mb
Release : 2015
Category : Nonlinear theories
ISBN : 1611220114

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Nonlinear Quantum Mechanics and Its Applications by Xiao-Feng Pang Pdf

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 : Krzysztof Kowalski
Publisher : World Scientific
Page : 148 pages
File Size : 53,9 Mb
Release : 1994
Category : Mathematics
ISBN : 9810217536

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Methods of Hilbert Spaces in the Theory of Nonlinear Dynamical Systems by Krzysztof Kowalski Pdf

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 : Panayotis G. Kevrekidis,Jesús Cuevas-Maraver,Avadh Saxena
Publisher : Springer Nature
Page : 389 pages
File Size : 52,8 Mb
Release : 2020-05-29
Category : Science
ISBN : 9783030449926

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Emerging Frontiers in Nonlinear Science by Panayotis G. Kevrekidis,Jesús Cuevas-Maraver,Avadh Saxena Pdf

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 : J. L. Gervais,Maurice Jacob
Publisher : World Scientific
Page : 538 pages
File Size : 46,6 Mb
Release : 1983
Category : Science
ISBN : 9971950642

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Non-linear and Collective Phenomena in Quantum Physics by J. L. Gervais,Maurice Jacob Pdf

http://www.worldscientific.com/worldscibooks/10.1142/0040

Author : Sandro Wimberger
Publisher : Springer
Page : 215 pages
File Size : 43,8 Mb
Release : 2014-05-13
Category : Science
ISBN : 9783319063430

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Nonlinear Dynamics and Quantum Chaos by Sandro Wimberger Pdf

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 : V. M. (Nitant) Kenkre
Publisher : Springer Nature
Page : 328 pages
File Size : 49,6 Mb
Release : 2022-03-26
Category : Science
ISBN : 9783030948115

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Interplay of Quantum Mechanics and Nonlinearity by V. M. (Nitant) Kenkre Pdf

This book presents an in-depth study of the discrete nonlinear Schrödinger equation (DNLSE), with particular emphasis on spatially small systems that permit analytic solutions. In many quantum systems of contemporary interest, the DNLSE arises as a result of approximate descriptions despite the fundamental linearity of quantum mechanics. Such scenarios, exemplified by polaron physics and Bose-Einstein condensation, provide application areas for the theoretical tools developed in this text. The book begins with an introduction of the DNLSE illustrated with the dimer, development of fundamental analytic tools such as elliptic functions, and the resulting insights into experiment that they allow. Subsequently, the interplay of the initial quantum phase with nonlinearity is studied, leading to novel phenomena with observable implications in fields such as fluorescence depolarization of stick dimers, followed by analysis of more complex and/or larger systems. Specific examples analyzed in the book include the nondegenerate nonlinear dimer, nonlinear trapping, rotational polarons, and the nonadiabatic nonlinear dimer. Phenomena treated include strong carrier-phonon interactions and Bose-Einstein condensation. This book is aimed at researchers and advanced graduate students, with chapter summaries and problems to test the reader’s understanding, along with an extensive bibliography. The book will be essential reading for researchers in condensed matter and low-temperature atomic physics, as well as any scientist who wants fascinating insights into the role of nonlinearity in quantum physics.

Author : Vasily Tarasov
Publisher : Elsevier
Page : 530 pages
File Size : 43,5 Mb
Release : 2008-06-06
Category : Science
ISBN : 0080559719

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Quantum Mechanics of Non-Hamiltonian and Dissipative Systems by Vasily Tarasov Pdf

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,Mark Hillery
Publisher : Cambridge University Press
Page : 385 pages
File Size : 43,9 Mb
Release : 2014-03-27
Category : Science
ISBN : 9781107004214

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The Quantum Theory of Nonlinear Optics by Peter D. Drummond,Mark Hillery Pdf

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 : Nicolae Alexandru Enachi
Publisher : Nova Science Publishers
Page : 0 pages
File Size : 54,6 Mb
Release : 2016
Category : Open systems (Physics)
ISBN : 163483321X

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Non-Linear Cooperative Effects in Open Quantum Systems by Nicolae Alexandru Enachi Pdf

This monograph, "Non-linear Cooperative Effects in Open Quantum Systems: Entanglement and Second Order Coherence" is dedicated to the large auditory of specialists interested in the modern approaches in quantum open systems, cooperative phenomena between excited atoms and the field of the non-linear interaction. Special attention is dedicated to the problems of non-linear interaction with vacuum fields and thermostat with finite temperature, but quantum aspects of laser generation of light in non-linear interaction with finite numbers of cavity modes remain the center of attention. In many situations, the limit to the traditional cooperative phenomena of open quantum systems and thermodynamics are taken into consideration. As the book contains the class of non-linear effects of generations of the particle in such cooperative phenomena, the author's aim was to describe squeezed problems and affect entanglement between the generation photons and phonons in cooperative processes. The new phenomenon of cooperative emission in the single- and two-quantum processes are carefully described for large audiences of specialists in the field of quantum optics and condensed matter physics, chemistry and biology.

Author : A Kundu
Publisher : CRC Press
Page : 320 pages
File Size : 43,7 Mb
Release : 2019-04-23
Category : Science
ISBN : 1420034618

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Classical and Quantum Nonlinear Integrable Systems by A Kundu Pdf

Covering both classical and quantum models, nonlinear integrable systems are of considerable theoretical and practical interest, with applications over a wide range of topics, including water waves, pin models, nonlinear optics, correlated electron systems, plasma physics, and reaction-diffusion processes. Comprising one part on classical theories

Author : Katsuhiro Nakamura
Publisher : CUP Archive
Page : 228 pages
File Size : 47,7 Mb
Release : 1994-06-02
Category : Mathematics
ISBN : 0521467462

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Quantum Chaos by Katsuhiro Nakamura Pdf

Past studies on chaos have been concerned with classical systems but this book is one of the first to deal with quantum chaos.

Author : Christophe Besse,Jean-Claude Garreau
Publisher : Springer
Page : 338 pages
File Size : 52,7 Mb
Release : 2015-08-26
Category : Science
ISBN : 9783319190150

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Nonlinear Optical and Atomic Systems by Christophe Besse,Jean-Claude Garreau Pdf

Focusing on the interface between mathematics and physics, this book offers an introduction to the physics, the mathematics, and the numerical simulation of nonlinear systems in optics and atomic physics. The text covers a wide spectrum of current research on the subject, which is an extremely active field in physics and mathematical physics, with a very broad range of implications, both for fundamental science and technological applications: light propagation in microstructured optical fibers, Bose-Einstein condensates, disordered systems, and the newly emerging field of nonlinear quantum mechanics. Accessible to PhD students, this book will also be of interest to post-doctoral researchers and seasoned academics.