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Nonlinear Adiabatic Evolution of Quantum Systems - Geometric Phase and Virtual Magnetic Monopole (Hardcover, 1st ed. 2018)
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Nonlinear Adiabatic Evolution of Quantum Systems - Geometric Phase and Virtual Magnetic Monopole (Hardcover, 1st ed. 2018)
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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 Schroedinger 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.
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