Nonlinear Adiabatic Evolution of Quantum Systems

1. Front Matter

   Pages i-ix

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2. Introduction to Adiabatic Evolution

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

   Pages 1-47

3. Nonlinear Adiabatic Evolution of Quantum Systems

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

   Pages 49-72

4. Quantum-Classical Correspondence of an Interacting Bosonic Many-Body System

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

   Pages 73-92

5. Exotic Virtual Magnetic Monopoles and Fields

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

   Pages 93-113

6. Applications of Nonlinear Adiabatic Evolution

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

   Pages 115-186

7. Back Matter

   Pages 187-190

   PDF

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.

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

“The book represents an almost exhaustive investigation of some very actual problems in non-linear adiabatic evolution of quantum systems. … It is expected to be a very useful tool for anybody working in the area of nonlinear quantum physics, from graduate students to scientific researchers.” (Alex B. Gaina, zbMATH 1405.81009, 2019)

• Institute of Applied Physics and Computational Mathematics, Beijing, China

  Jie Liu

• Xi'an Jiaotong University, Xi'an, China

  Sheng-Chang Li

• China Academy of Engineering Physics, Beijing, China

  Li-Bin Fu

• Institute of Applied Physics and Computational Mathematics, Beijing, China

  Di-Fa Ye

Jie Liu is a professor at the Institute of Applied Physics and Computational Mathematics, Beijing. He obtained his bachelor’s and doctoral degrees in 1986 and 1991, both from Nanjing University. Dr. Liu has an international reputation in many interdisciplinary scientific and technical areas such as adiabatic quantum theory, cold-atom physics, strong-field physics, and laser-driven inertial confinement fusion. He has led more than 15 national research projects, including projects of the National High Technology Research and Development Program, the National Key Basic Research and Development Program, and the National Natural Science Foundation of China, authored 4 monographs, and published over 200 peer-reviewed journal articles with more than 3500 citations. 


Sheng-Chang Li is an associate professor at Xi’an Jiaotong University, Xi’an. He obtained his bachelor’s degree in 2006 from Northwest Normal University and his doctoral degree in 2012 from the Graduate School, China Academy of Engineering Physics. He has been working on nonlinear dynamics and quantum adiabatic theory of complex systems such as cold atoms, Bose-Einstein condensation, and plasmas. He has led more than 5 scientific research projects, including projects of the Natural Science Foundation of China, the Natural Science Fundamental Research Program of Shaanxi Province of China, and the Fundamental Research Funds for the Central Universities of China. He has published over 30 peer-reviewed journal articles, which have been cited more than 300 times in total and his personal research H-index is 11.


Li-Bin Fu is a professor of the Department of Physics, Graduate School of China Academy of Engineering Physics. He obtained his bachelor’s and doctoral degrees in 1994 and 1999, both from Lanzhou University. He was a postdoctoral scholar (1999-2001), associate professor (2001-2005), and professor (2005-2017) at the Institute of Applied Physics and Computational Mathematics, Beijing. He was an Alexander von Humboldt Scholar between 2003 and 2004 at the Max Plank Institute for Physics of Complex Systems in Germany. Dr. Fu has achieved many distinctive and well-recognized academic accomplishments in strong-field physics and in quantum physics, and published over 150 peer-reviewed journal articles. 


Di-Fa Ye is an associate professor at the Institute of Applied Physics and Computational Mathematics, Beijing. He obtained his bachelor’s degree in 2005 from Xiamen University and his doctoral degree in 2011 from the Graduate School, China Academy of Engineering Physics. He was an Alexander von Humboldt Scholar between 2011 and 2012 at the Max Plank Institute for Nuclear Physics in Germany. His main research interest covers cold-atom physics, strong-field physics and attosecond optics. He has published 30 peer-reviewed journal articles, which have been cited over 600 times in total.

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