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BL
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| Record Number
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891586
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| Main Entry
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Liu, Jie
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| Title & Author
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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.
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| Publication Statement
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Singapore :: Springer,, [2018]
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| Page. NO
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1 online resource
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| ISBN
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9789811326431
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: 9789811326448
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: 9811326436
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: 9811326444
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9789811326424
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9811326428
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| Contents
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Intro; Preface; Contents; 1 Introduction to Adiabatic Evolution; 1.1 Classical Adiabatic Motion; 1.1.1 Classical Adiabatic Invariant; 1.1.2 Adiabatic Geometric Angle-Hannay Angle; 1.1.3 Example I: One-Dimensional Harmonic Oscillator; 1.1.4 Example II: Celestial Two-Body Problem; 1.1.5 Example III: Foucault Pendulum; 1.2 Quantum Adiabatic Evolution; 1.2.1 Quantum Adiabatic Theorem; 1.2.2 Adiabatic Geometric Phase-Berry Phase; 1.2.3 Virtual Magnetic Monopole; 1.2.4 Nonadiabatic Geometric Phase-Aharonov-Anandan Phase; 1.2.5 Example I: Born-Oppenheimer Approximation.
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1.2.6 Example II: Aharonov-Bohm Effect1.2.7 Example III: Adiabatic Quantum Computing; 1.2.8 Example IV: Geometric Quantum Computation; 1.2.9 Example V: Superadiabatic Quantum Driving; 1.3 Classical-Quantum Correspondence; 1.3.1 Bohr-Sommerfeld Quantization Rule; 1.3.2 Relation Between the Berry Phase and the Hannay Angle; 1.3.3 Nonadiabatic Geometric Phase and Hannay Angle in the Generalized Harmonic Oscillator; References; 2 Nonlinear Adiabatic Evolution of Quantum Systems; 2.1 Physical Origins of Nonlinearity; 2.1.1 Nonlinear Gross-Pitaevskii (GP) Equation; 2.1.2 Nonlinear Optical Fibers.
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2.1.3 Nonlinear Atom-Molecule Conversion2.2 Nonlinear Adiabatic Evolution of Quantum States; 2.2.1 General Formalism; 2.2.2 Eigenstates; 2.2.3 Cyclic and Quasicyclic States; 2.2.4 Two-Level Model Illustration; 2.3 Nonlinear Adiabatic Geometric Phase; 2.3.1 Adiabatic Parameter Expansion; 2.3.2 Projective Hilbert Space Description; 2.3.3 Nonlinear Adiabatic Geometric Phase; 2.3.4 Two-Mode Model Illustration; References; 3 Quantum-Classical Correspondence of an Interacting Bosonic Many-Body System; 3.1 Commutability Between the Semiclassical Limit and the Adiabatic Limit; 3.1.1 Hamiltonian.
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3.1.2 Semiclassical Limit and Adiabatic Limit3.1.3 Tunneling Rates; 3.1.4 Energy Band Structure; 3.1.5 Commutability Between Two Limits; 3.2 Quantum-Classical Correspondence of the Adiabatic Geometric Phase; 3.2.1 Interacting Bosonic Many-Body System; 3.2.2 Mean-Field Hamiltonian; 3.2.3 Quantum Berry Phase; 3.2.4 Classical Hannay Angle; 3.2.5 Connection Between the Berry Phase and the Hannay Angle; References; 4 Exotic Virtual Magnetic Monopoles and Fields; 4.1 Disk-Shaped Virtual Magnetic Field; 4.2 Fractional Virtual Magnetic Monopole; 4.3 Virtual Magnetic Monopole Chain; References.
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5 Applications of Nonlinear Adiabatic Evolution5.1 Nonlinear Coherent Optical Coupler; 5.2 Nonlinear Landau-Zener Tunneling; 5.2.1 Two-Level System; 5.2.2 Three-Level System; 5.2.3 Spatially Magnetic Modulated Trap; 5.3 Nonlinear Rosen-Zener Tunneling; 5.4 Nonlinear Ramsey Interferometry; 5.5 Nonlinear Atom-Molecule Conversion; 5.5.1 Bosonic Atoms to Bosonic Molecules; 5.5.2 Fermionic Atoms to Bosonic Molecules; 5.6 Nonlinear Composite Adiabatic Passage; References; Index.
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| Abstract
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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 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.
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| Subject
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Adiabatic invariants.
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Geometric quantum phases.
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Adiabatic invariants.
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Atomic molecular physics.
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Geometric quantum phases.
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Quantum physics (quantum mechanics quantum field theory)
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SCIENCE-- Energy.
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SCIENCE-- Mechanics-- General.
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SCIENCE-- Physics-- General.
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Statistical physics.
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| Dewey Classification
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530.12
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| LC Classification
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QC20.7.A34L58 2018
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