Nonlinear Adiabatic Evolution Of Quantum Systems

Author : Jie Liu
Publisher : Springer
ISBN 13 : 9811326436
Total Pages : 190 pages
Book Rating : 4.31/5 ( download)

DOWNLOAD NOW!

Download or read book Nonlinear Adiabatic Evolution of Quantum Systems written by Jie Liu and published by Springer. This book was released on 2018-09-03 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Jie Liu
Publisher :
ISBN 13 : 9789811326448
Total Pages : pages
Book Rating : 4.44/5 ( download)

DOWNLOAD NOW!

Download or read book Nonlinear Adiabatic Evolution of Quantum Systems written by Jie Liu and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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

DOWNLOAD NOW!

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 : Xiao-Feng Pang
Publisher : World Scientific
ISBN 13 : 9812561161
Total Pages : 644 pages
Book Rating : 4.69/5 ( download)

DOWNLOAD NOW!

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 644 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 : Qian Niu
Publisher : World Scientific
ISBN 13 : 9813225726
Total Pages : 424 pages
Book Rating : 4.25/5 ( download)

DOWNLOAD NOW!

Download or read book Physical Effects of Geometric Phases written by Qian Niu and published by World Scientific. This book was released on 2017-08-28 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Heinz-dietrich Doebner
Publisher : World Scientific
ISBN 13 : 981454924X
Total Pages : 494 pages
Book Rating : 4.40/5 ( download)

DOWNLOAD NOW!

Download or read book Nonlinear, Deformed And Irreversible Quantum Systems - Proceedings Of The International Symposium On Mathematical Physics written by Heinz-dietrich Doebner and published by World Scientific. This book was released on 1995-08-31 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : James E. Bayfield
Publisher : Wiley-VCH
ISBN 13 :
Total Pages : 408 pages
Book Rating : 4.64/5 ( download)

DOWNLOAD NOW!

Download or read book Quantum Evolution written by James E. Bayfield and published by Wiley-VCH. This book was released on 1999-09-15 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : V. M. (Nitant) Kenkre
Publisher : Springer Nature
ISBN 13 : 3030948110
Total Pages : 328 pages
Book Rating : 4.15/5 ( download)

DOWNLOAD NOW!

Download or read book Interplay of Quantum Mechanics and Nonlinearity written by V. M. (Nitant) Kenkre and published by Springer Nature. This book was released on 2022-03-26 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Amnon Kohen
Publisher : CRC Press
ISBN 13 : 1420028022
Total Pages : 1092 pages
Book Rating : 4.27/5 ( download)

DOWNLOAD NOW!

Download or read book Isotope Effects In Chemistry and Biology written by Amnon Kohen and published by CRC Press. This book was released on 2005-11-01 with total page 1092 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of isotope effects has expanded exponentially in the last decade, and researchers are finding isotopes increasingly useful in their studies. Bringing literature on the subject up to date, Isotope Effects in Chemistry and Biology covers current principles, methods, and a broad range of applications of isotope effects in the physical, biolo

Author : Linda Reichl
Publisher : Springer Science & Business Media
ISBN 13 : 1475743505
Total Pages : 692 pages
Book Rating : 4.00/5 ( download)

DOWNLOAD NOW!

Download or read book The Transition to Chaos written by Linda Reichl and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 692 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on courses given at the universities of Texas and California, this book treats an active field of research that touches upon the foundations of physics and chemistry. It presents, in as simple a manner as possible, the basic mechanisms that determine the dynamical evolution of both classical and quantum systems in sufficient generality to include quantum phenomena. The book begins with a discussion of Noether's theorem, integrability, KAM theory, and a definition of chaotic behavior; continues with a detailed discussion of area-preserving maps, integrable quantum systems, spectral properties, path integrals, and periodically driven systems; and concludes by showing how to apply the ideas to stochastic systems. The presentation is complete and self-contained; appendices provide much of the needed mathematical background, and there are extensive references to the current literature; while problems at the ends of chapters help students clarify their understanding. This new edition has an updated presentation throughout, and a new chapter on open quantum systems.