Nonlinear Adiabatic Evolution of Quantum Systems
Geometric Phase and Virtual Magnetic Monopole
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Beschreibung
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.
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.
Offers a detailed introduction and comprehensive description of nonlinear adiabatic evolution theory Provides an effective method for the description of adiabatic evolution of interacting many-body systems Presents numerous applications of nonlinear adiabatic evolution theory for various problems of theoretical physics
Autor*in
Jie Liu
Themen in »Nonlinear Adiabatic Evolution of Quantum Systems«
Adiabatic invariant Interacting many-body system Adiabatic geometric phase Nonlinear Schrodinger equation Hannay angle Virtual magnetic field Berry phase
Stimmen zu »Nonlinear Adiabatic Evolution of Quantum Systems«
“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)
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