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作者 Gumbs, Godfrey
書名 Properties of Interacting Low-Dimensional Systems
出版項 Somerset : John Wiley & Sons, Incorporated, 2011
©2013
國際標準書號 9783527638178 (electronic bk.)
9783527408948
book jacket
版本 1st ed
說明 1 online resource (393 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
附註 Intro -- Title Page -- Contents -- Preface -- References -- Part One Linear Response of Low Dimensional Quantum Systems -- 1 Introduction -- 1.1 Second-Quantized Representation for Electrons -- 1.2 Second Quantization and Fock States -- 1.3 The Boson Case -- 1.4 The Fermion Case -- 1.5 The Hamiltonian of Electrons -- 1.6 Electron-Phonon Interaction -- 1.7 Effective Electron-Electron Interaction -- 1.8 Degenerate Electron Gases -- 1.9 Ground-State Energy in the High Density Limit -- 1.10 Wigner Solid -- 1.11 The Chemical Potential of an Ideal Bose Gas and Bose-Einstein Condensation -- 1.12 Problems -- References -- 2 The Kubo-Greenwood Linear Response Theory -- 2.1 Fluctuations and Dissipation -- 2.2 Nyquist's Relation -- 2.3 Linear Response Theory -- 2.3.1 Generalized Susceptibility -- 2.3.2 Kronig-Kramers Relations -- 2.3.3 Dielectric Function in Three Dimensions -- 2.4 The Density Matrix and Quantum Statistics -- 2.4.1 The von Neumann Density Matrix -- 2.4.2 Entropy -- 2.5 Kubo's Theory -- 2.6 The Kubo Equation -- 2.7 Fluctuation-Dissipation Theorem -- 2.8 Applications -- 2.8.1 Mobility and the Nernst-Einstein Relation -- 2.8.2 Electrical Conductivity and the Nyquist Relation -- 2.8.3 Magnetic Susceptibility -- 2.8.4 The Langevin Equation -- 2.8.5 Stochastic Model of Magnetic Resonance -- 2.8.6 Gaussian Process -- 2.9 Kinetic Equation for Elastic Processes -- 2.9.1 Boltzmann's Transport Equation -- 2.9.2 The Collision Term -- 2.9.3 Solution in the Ohmic Regime -- 2.9.4 Conductivity and Mobility -- 2.10 Problems -- References -- 3 Feynman Diagrammatic Expansion -- 3.1 General Formalism -- 3.2 Functional Derivative Techniques -- 3.3 Unrenormalized Expansion for G and Σ -- 3.4 Renormalized Expansion for Self-Energy Σ -- 3.5 The Schrödinger Equation in the Hartree-Fock Approximation -- 3.6 Screened External Potential
3.7 Retarded Polarization Function -- 3.8 RPA for the Polarization Function -- 3.9 Problems -- References -- 4 Plasmon Excitations in Mesoscopic Structures -- 4.1 Linear Response Theory and Collective Excitations -- 4.1.1 Screening and the Self-Consistent Field Approximation -- 4.2 A Linear Array of Nanotubes -- 4.2.1 Tight-Binding Model -- 4.2.2 Numerical Results and Discussion -- 4.3 A Linear Array of Quantum Wires -- 4.4 Coupled Half-Plane Superlattices -- 4.4.1 Hydrodynamic Model -- 4.4.2 Numerical Results and Discussion -- 4.5 Problems -- References -- 5 The Surface Response Function, Energy Loss and Plasma Instability -- 5.1 Surface Response Function -- 5.1.1 The Image Potential -- 5.1.2 A Bi-Layer System -- 5.1.3 A Dielectric Slab -- 5.1.4 A Layered 2DEG System -- 5.2 Electron Energy Loss for a Planar Surface -- 5.2.1 Transfer-Matrix Method -- 5.2.2 Motion Parallel to the Surface -- 5.2.3 Motion Perpendicular to the Surface -- 5.2.4 The Inverse Dielectric Function Formalism -- 5.3 Plasma Instability for a Planar Surface -- 5.4 Energy Transfer in Nanotubes -- 5.4.1 Energy Loss on a Single Wall Nanotube -- 5.5 Problems -- References -- 6 The Rashba Spin-Orbit Interaction in 2DEG -- 6.1 Introduction to Spin-Orbit Coupling -- 6.2 Spin-Orbit Coupling in the Dirac Equation -- 6.3 Rashba Spin-Orbit Coupling for a Quantum Wire -- 6.4 SOI Effects on Conductance and Electron-Diffusion Thermoelectric Power -- 6.5 Problems -- References -- 7 Electrical Conductivity: the Kubo and Landauer-Büttiker Formulas -- 7.1 Quantum Mechanical Current -- 7.2 The Statistical Current -- 7.3 A Green's Function Formalism -- 7.4 The Static Limit -- 7.5 Model and Single-Particle Eigenstates -- 7.6 Averaged Conductivity -- 7.7 Applications to One-Dimensional Density Modulated 2DEG -- 7.8 Scattering Theory Formalism -- 7.9 Quantum Hall Effect -- 7.10 Problems -- References
8 Nonlocal Conductivity for a Spin-Split Two-Dimensional Electron Liquid -- 8.1 Introduction -- 8.2 Kubo Formula for Conductivity -- 8.3 The Self-Energy and Scattering Time -- 8.4 Drude-Type Conductivity for Spin-Split Subband Model -- 8.5 Vertex Corrections to the Local Conductivity -- 8.6 Numerical Results for Scattering Times -- 8.7 Related Results in 3D in the Absence of SOI -- References -- 9 Integer Quantum Hall Effect -- 9.1 Basic Principles of the Integer Quantum Hall Effect -- 9.1.1 The Hall Effect -- 9.1.2 The Quantum Hall Effect -- 9.1.3 An Idealized Model -- 9.1.4 Effect of Finite Temperature -- 9.1.5 Effect of Impurities -- 9.1.6 Application of the Quantum Hall Effect -- 9.2 Fundamental Theories of the IQHE -- 9.2.1 Energy Spectrum and Wave functions -- 9.2.2 Perturbation and Scattering Theory -- 9.2.3 Gauge Symmetry Approach -- 9.2.4 The QHE in a Periodic Potential -- 9.2.5 Topological Equivalence of the Quantum Hall Conductance -- 9.3 Corrections to the Quantization of the Hall Conductance -- 9.3.1 Properties of the Green's Function -- References -- 10 Fractional Quantum Hall Effect -- 10.1 The Laughlin Ground State -- 10.1.1 The Lowest Landau Level -- 10.1.2 Laughlin's Wave Function -- 10.1.3 Properties of the Laughlin Wave Function -- 10.1.4 Justification of the Laughlin State -- 10.2 Elementary Excitations -- 10.2.1 Fractional Charge -- 10.2.2 The Complete Set of Quasi-Hole States -- 10.3 The Ground State: Degeneracy and Ginzburg-Landau Theory -- 10.3.1 Ground State Degeneracy -- 10.3.2 Ginzburg-Landau Theory of the Quantum Hall Effect -- 10.4 Problems -- References -- 11 Quantized Adiabatic Charge Transport in 2D Electron Systems and Nanotubes -- 11.1 Introduction -- 11.2 Theory for Current Quantization -- 11.3 Tunneling Probability and Current Quantization for Interacting Two-Electron System -- 11.3.1 Spin Unpolarized Case
11.4 Adiabatic Charge Transport in Carbon Nanotubes -- 11.5 Summary and Remarks -- References -- 12 Graphene -- 12.1 Introduction -- 12.2 Electronic Properties of Graphene -- 12.3 Graphene Nanoribbons and Their Spectrum -- 12.3.1 Zigzag Edge -- 12.3.2 Armchair Nanoribbon -- 12.4 Valley-Valve Effect and Perfect Transmission in GNR's -- 12.5 GNR's Electronic and Transport Properties in External Fields -- 12.6 Problems -- Appendix 12.A Energy Eigen States -- Appendix 12.B The Conductance -- References -- 13 Semiclassical Theory for Linear Transport of Electrons -- 13.1 Roughness Scattering -- 13.1.1 Model for Elastic Scattering -- 13.1.2 Numerical Results for Roughness Scattering Effect -- 13.2 Phonon Scattering -- 13.2.1 Model for Inelastic Scattering -- 13.2.2 Numerical Results for Phonon Scattering Effect -- 13.3 Thermoelectric Power -- 13.3.1 Model for Non-equilibrium Phonons -- 13.3.2 Numerical Results for Thermoelectric Power -- 13.4 Electron-Electron Scattering -- 13.4.1 Model for Pair Scattering -- 13.4.2 Numerical Results for Coulomb Scattering Effect -- References -- Part Two Nonlinear Response of Low Dimensional Quantum Systems -- 14 Theory for Nonlinear Electron Transport -- 14.1 Semiclassical Theory -- 14.1.1 Transient Boltzmann Equation -- 14.1.2 Numerical Procedure -- 14.1.3 Numerical Results for Bloch Oscillations and Dynamical Localization -- 14.2 Quantum Theory -- 14.2.1 Force Balance Equation -- 14.2.2 Boltzmann Scattering Equation -- References -- 15 Spontaneous and Stimulated Nonlinear Wave Mixing of Multi-excitons -- 15.1 Spontaneous, Stimulated, Coherent and Incoherent Nonlinear Wave Mixing -- 15.2 n + 1 Wave Mixing in QD Fluids and Polymer QDs Molecule Solutions -- 15.2.1 Stimulated and Spontaneous Incoherent Signals -- 15.2.2 Spontaneous Coherent Signal -- 15.3 Application to Two-Photon-Induced Signals
Appendix 15.A Semiclassical vs. Quantum Field Derivation of Heterodyne Detected Signals -- Appendix 15.B Generalized Susceptibility and Its CTPL Representation -- References -- 16 Probing Excitons and Biexcitons in Coupled QDs by Coherent Optical Spectroscopy -- 16.1 Model Hamiltonian for Two Coupled Quantum Dots -- 16.2 Single-exciton Manifold and the Absorption Spectrum -- 16.3 Two-exciton Manifold and the 2D Spectra -- 16.4 Summary -- Appendix 16.A Transformation of the Electron-Hole Hamiltonian Using Excitonic Variables -- Appendix 16.B The Nonlinear Exciton Equations -- Appendix 16.C The 2D Signals -- References -- 17 Non-thermal Distribution of Hot Electrons -- 17.1 Introduction -- 17.2 Boltzmann Scattering Equation -- 17.3 Numerical Results for Effective Electron Temperature -- 17.4 Summary -- References -- Index
Filling the gap for comprehensive coverage of the realistic fundamentals and approaches needed to perform cutting-edge research on mesoscopic systems, this textbook allows advanced students to acquire and use the skills at a highly technical, research-qualifying level. Starting with a brief refresher to get all readers on an equal footing, the text moves on to a broad selection of advanced topics, backed by problems with solutions for use in classrooms as well as for self-study. Written by authors with research and teaching backgrounds from eminent institutions and based on a tried-and-tested lecture, this is a must-have for researchers, research students and instructors involved with semiconductor junctions, nanostructures and thin film systems
Description based on publisher supplied metadata and other sources
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
鏈接 Print version: Gumbs, Godfrey Properties of Interacting Low-Dimensional Systems Somerset : John Wiley & Sons, Incorporated,c2011 9783527408948
主題 Low-dimensional semiconductors
Electronic books
Alt Author Huang, Danhong
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