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Nonlinear Adiabatic Evolution of Quantum Systems

Geometric Phase and Virtual Magnetic Monopole

  • Jie Liu
  • Sheng-Chang Li
  • Li-Bin Fu
  • Di-Fa Ye

Table of contents

  1. Front Matter
    Pages i-ix
  2. Jie Liu, Sheng-Chang Li, Li-Bin Fu, Di-Fa Ye
    Pages 1-47
  3. Jie Liu, Sheng-Chang Li, Li-Bin Fu, Di-Fa Ye
    Pages 49-72
  4. Jie Liu, Sheng-Chang Li, Li-Bin Fu, Di-Fa Ye
    Pages 73-92
  5. Jie Liu, Sheng-Chang Li, Li-Bin Fu, Di-Fa Ye
    Pages 93-113
  6. Jie Liu, Sheng-Chang Li, Li-Bin Fu, Di-Fa Ye
    Pages 115-186
  7. Back Matter
    Pages 187-190

About this book

Introduction

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.

Keywords

Adiabatic invariant Interacting many-body system Adiabatic geometric phase Nonlinear Schrodinger equation Hannay angle Virtual magnetic field Berry phase

Authors and affiliations

  • Jie Liu
    • 1
  • Sheng-Chang Li
    • 2
  • Li-Bin Fu
    • 3
  • Di-Fa Ye
    • 4
  1. 1.Institute of Applied Physics and Computational MathematicsBeijingChina
  2. 2.Xi'an Jiaotong UniversityXi'anChina
  3. 3.China Academy of Engineering PhysicsBeijingChina
  4. 4.Institute of Applied Physics and Computational Mathematics BeijingChina

Bibliographic information

  • DOI https://doi.org/10.1007/978-981-13-2643-1
  • Copyright Information Springer Nature Singapore Pte Ltd. 2018
  • Publisher Name Springer, Singapore
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-981-13-2642-4
  • Online ISBN 978-981-13-2643-1
  • Buy this book on publisher's site