Nonlinear Adiabatic Evolution of Quantum Systems
Title | Nonlinear Adiabatic Evolution of Quantum Systems PDF eBook |
Author | Jie Liu |
Publisher | Springer |
Pages | 197 |
Release | 2018-09-03 |
Genre | Science |
ISBN | 9811326436 |
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
Title | Nonlinear Adiabatic Evolution of Quantum Systems PDF eBook |
Author | Jie Liu |
Publisher | |
Pages | |
Release | 2018 |
Genre | Adiabatic invariants |
ISBN | 9789811326448 |
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
Title | Nonlinear, Deformed And Irreversible Quantum Systems - Proceedings Of The International Symposium On Mathematical Physics PDF eBook |
Author | Heinz-dietrich Doebner |
Publisher | World Scientific |
Pages | 494 |
Release | 1995-08-31 |
Genre | |
ISBN | 981454924X |
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.
Physical Effects of Geometric Phases
Title | Physical Effects of Geometric Phases PDF eBook |
Author | Qian Niu |
Publisher | World Scientific |
Pages | 424 |
Release | 2017-08-28 |
Genre | Science |
ISBN | 9813225726 |
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.
Quantum Mechanics in Nonlinear Systems
Title | Quantum Mechanics in Nonlinear Systems PDF eBook |
Author | Xiao-Feng Pang |
Publisher | World Scientific |
Pages | 644 |
Release | 2005 |
Genre | Science |
ISBN | 9812561161 |
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 Evolution
Title | Quantum Evolution PDF eBook |
Author | James E. Bayfield |
Publisher | Wiley-VCH |
Pages | 408 |
Release | 1999-09-15 |
Genre | Science |
ISBN |
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.
Nonlinear Waves: Classical and Quantum Aspects
Title | Nonlinear Waves: Classical and Quantum Aspects PDF eBook |
Author | Fatkhulla Abdullaev |
Publisher | Springer Science & Business Media |
Pages | 563 |
Release | 2006-03-02 |
Genre | Science |
ISBN | 1402021909 |
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.