Nonlinear Adiabatic Evolution Of Quantum Systems
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Nonlinear Adiabatic Evolution Of Quantum Systems
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Author : Jie Liu
language : en
Publisher: Springer
Release Date : 2018-09-03
Nonlinear Adiabatic Evolution Of Quantum Systems written by Jie Liu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-03 with Science categories.
This book systematically introduces the nonlinear adiabatic evolution theory of quantum many-body systems. The nonlinearity stems from a mean-field treatment of the interactions between particles, and the adiabatic dynamics of the system can be accurately described by the nonlinear Schrödinger equation. The key points in this book include the adiabatic condition and adiabatic invariant for nonlinear system; the adiabatic nonlinear Berry phase; and the exotic virtual magnetic field, which gives the geometric meaning of the nonlinear Berry phase. From the quantum-classical correspondence, the linear and nonlinear comparison, and the single particle and interacting many-body difference perspectives, it shows a distinct picture of adiabatic evolution theory. It also demonstrates the applications of the nonlinear adiabatic evolution theory for various physical systems. Using simple models it illustrates the basic points of the theory, which are further employed for the solution of complex problems of quantum theory for many-particle systems. The results obtained are supplemented by numerical calculations, presented as tables and figures.
Nonlinear Adiabatic Evolution Of Quantum Systems
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Author : Jie Liu
language : en
Publisher:
Release Date : 2018
Nonlinear Adiabatic Evolution Of Quantum Systems written by Jie Liu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Adiabatic invariants categories.
This book systematically introduces the nonlinear adiabatic evolution theory of quantum many-body systems. The nonlinearity stems from a mean-field treatment of the interactions between particles, and the adiabatic dynamics of the system can be accurately described by the nonlinear Schrödinger equation. The key points in this book include the adiabatic condition and adiabatic invariant for nonlinear system; the adiabatic nonlinear Berry phase; and the exotic virtual magnetic field, which gives the geometric meaning of the nonlinear Berry phase. From the quantum-classical correspondence, the linear and nonlinear comparison, and the single particle and interacting many-body difference perspectives, it shows a distinct picture of adiabatic evolution theory. It also demonstrates the applications of the nonlinear adiabatic evolution theory for various physical systems. Using simple models it illustrates the basic points of the theory, which are further employed for the solution of complex problems of quantum theory for many-particle systems. The results obtained are supplemented by numerical calculations, presented as tables and figures.
Nonlinear Deformed And Irreversible Quantum Systems Proceedings Of The International Symposium On Mathematical Physics
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Author : Heinz-dietrich Doebner
language : en
Publisher: World Scientific
Release Date : 1995-08-31
Nonlinear Deformed And Irreversible Quantum Systems Proceedings Of The International Symposium On Mathematical Physics written by Heinz-dietrich Doebner and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-08-31 with categories.
In recent years nonlinear and irreversible quantum mechanics is becoming increasingly important because of the availability of precision experiments. There are new and successful attempts to understand quantum irreversibility. The development of generalized symmetries has to led to new families of evolution equations for pure and mixed states. On the one hand, this timely symposium covers nonlinear and irreversible quantum mechanics, the theory of quantization methods, causality and various problems important in this context. On the other hand, it reports the development of quantum group symmetries, and of methods to construct deformed quantum mechanical evolution equations like the q-deformed Schrödinger equations.
Quantum Mechanics In Nonlinear Systems
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Author : Xiao-Feng Pang
language : en
Publisher: World Scientific
Release Date : 2005
Quantum Mechanics In Nonlinear Systems written by Xiao-Feng Pang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Science categories.
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.
Quantum Mechanics And Nonlinear Waves
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Author : Philip Barnes Burt
language : en
Publisher: CRC Press
Release Date : 1981
Quantum Mechanics And Nonlinear Waves written by Philip Barnes Burt and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Science categories.
Interplay Of Quantum Mechanics And Nonlinearity
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Author : V. M. (Nitant) Kenkre
language : en
Publisher: Springer Nature
Release Date : 2022-03-26
Interplay Of Quantum Mechanics And Nonlinearity written by V. M. (Nitant) Kenkre and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-26 with Science categories.
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.
Quantum Evolution
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Author : James E. Bayfield
language : en
Publisher: Wiley-VCH
Release Date : 1999-09-15
Quantum Evolution written by James E. Bayfield and has been published by Wiley-VCH this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-09-15 with Science categories.
A unique introduction to the concepts of quantum mechanics, Quantum Evolution addresses the present status of time-dependent quantum mechanics for few-body systems with electromagnetic interactions. It bridges between the quantum mechanics of stationary quantum systems and a number of recent advanced theoretical treatises on various aspects of quantum mechanics. The focus is on strongly-quantum and semi-classical systems, including the quantum manifestations of orderly and chaotic nonlinear classical dynamics.
Physical Effects Of Geometric Phases
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Author : Qian Niu
language : en
Publisher: World Scientific
Release Date : 2017-08-28
Physical Effects Of Geometric Phases written by Qian Niu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-28 with Science categories.
Berry phase has been widely used in condensed matter physics in the past two decades. This volume is a timely collection of essential papers in this important field, which is highlighted by 2016 Nobel Prize in physics and recent exciting developments in topological matters. Each chapter has an introduction, which helps readers to understand the reprints that follow.
Nonlinear Waves Classical And Quantum Aspects
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Author : Fatkhulla Abdullaev
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-02
Nonlinear Waves Classical And Quantum Aspects written by Fatkhulla Abdullaev 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 2006-03-02 with Science categories.
Leading scientists discuss the most recent physical and experimental results in the physics of Bose-Einstein condensate theory, the theory of nonlinear lattices (including quantum and nonlinear lattices), and nonlinear optics and photonics. Classical and quantum aspects of the dynamics of nonlinear waves are considered. The contributions focus on the Gross-Pitaevskii equation and on the quantum nonlinear Schrödinger equation. Recent experimental results on atomic condensates and hydrogen bonded systems are reviewed. Particular attention is given to nonlinear matter waves in periodic potential.
Towards A Nonlinear Quantum Physics
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Author : J. R. Croca
language : en
Publisher: World Scientific
Release Date : 2003
Towards A Nonlinear Quantum Physics written by J. R. Croca and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Science categories.
The author of this book presents conceptual and experimental evidence showing that Heisenberg''s uncertainty relations are not valid in all cases. Furthermore, he derives a more general set of uncertainty relations. The new relations result from the replacement of the Fourier nonlocal and nontemporal paradigm by wavelet local analysis. These results lead to a coherent and beautiful causal synthesis unifying quantum and classical physics.