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Nonlinear adiabatic evolution of quantum systems : geometric phase and virtual magnetic monopole

Author: Jie Liu
Publisher: Singapore : Springer, [2018]
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
(OCoLC)1048945444
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Jie Liu
ISBN: 9789811326431 9811326436
OCLC Number: 1050614588
Description: 1 online resource
Contents: 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. 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. 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. 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. 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.
Responsibility: Jie Liu, Sheng-Chang Li, Li-Bin Fu, Di-Fa Ye.

Abstract:

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,  Read more...

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