Introduction to Wave Scattering, Localization and Mesoscopic Phenomena
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1 Springer Series in Materials Science 88 Introduction to Wave Scattering, Localization and Mesoscopic Phenomena Bearbeitet von Ping Sheng Neuausgabe Buch. xv, 329 S. Hardcover ISBN Format (B x L): 15,5 x 23,5 cm Weitere Fachgebiete > Technik > Technik Allgemein > Physik, Chemie für Ingenieure Zu Leseprobe schnell und portofrei erhältlich bei Die Online-Fachbuchhandlung beck-shop.de ist spezialisiert auf Fachbücher, insbesondere Recht, Steuern und Wirtschaft. Im Sortiment finden Sie alle Medien (Bücher, Zeitschriften, CDs, ebooks, etc.) aller Verlage. Ergänzt wird das Programm durch Services wie Neuerscheinungsdienst oder Zusammenstellungen von Büchern zu Sonderpreisen. Der Shop führt mehr als 8 Millionen Produkte.
2 Contents 1 Introduction RelevantLengthScales DiffusiveTransport Coherent Backscattering and the Approach to Localization Sample Size Dependence Localization and Scaling Spatial Dimensionality in Localization and Diffusion MesoscopicPhenomena Localization vs. Confinement TopicsnotCovered Quantum and Classical Waves Preliminaries Quantum and Classical Wave Equations Green Functions for Waves in a Uniform Medium Green Function for the Uniform Medium Green Function and the Density of States Real Space Green Functions Waves on a Discrete Lattice Dispersion Relation Random Discrete Lattices: the Anderson Model Lattice Green Functions D Lattice Green Function D Lattice Green Function D Lattice Green Function Treating Continuum Problems on a Lattice Problems and Solutions Wave Scattering and the Coherent Potential Approximation AnOverviewoftheApproach... 45
3 X Contents Information from the First Moment Information from the Second Moment Information from Higher Moments Wave Scattering Formalism The Operator Notation The T Operator Configurational Averaging The Self-Energy Single Scatterer: the Lattice Case Impurity Bound State Single Scatterer: the Continuum Case Wave Function in the Single Scatterer Case A Digression on Notation Scattering Amplitude and the t Operator Scattering Amplitude and the Optical Theorem: 3DCase Scattering Amplitude and the Optical Theorem: 2DCase Scattering Amplitude and the Optical Theorem: 1DCase Infinite Number of Scatterers: the Effective Medium Meaning of a k-independent Self Energy The Mean Free Path The Coherent Potential Approximation (CPA) Accuracy of the CPA Coherent Waves and Effective Media Coherence and Homogenization CPA: The Anderson Model Efficient Green Function Evaluation from DOS CPA:TheClassicalWaves The Role of Microstructure The Symmetric Microstructure The Dispersion Microstructure Effective Medium Modeling of Inhomogeneous Materials Granular Metals Sedimentary Rocks The Spectral Function Approach: Coherent Quasimodes Formulation Coherent Acoustic Waves in the Intermediate Wavelength Regime Novel Acoustic Modes in Colloidal Suspensions Group Velocity in Strongly Scattering Media Accuracy of the Spectral Function Approach
4 Contents XI 5 Diffusive Waves Beyond the Coherent Regime Pulse Intensity Evolution in a Random Medium The Bethe-Salpeter Equation and its Solution by Moments Notations Irreducible Vertex Function and the Bethe Salpeter Equation Diffusive Behavior from a Simplified Model The Ward Identity in the Simplified Model Formal Derivation of the Diffusive Pole andthediffusionconstant Higher Moment of the Transport Equation Expansion of φ k Solution for the Diffusive Pole and the Diffusion Constant Configurational Averaging and Dissipation The Vertex Function The Reducible Vertex and Diagrammatic Representations CPA for Γ: the Ladder Diagrams and the Irreducible Vertex Irreducible Vertex: the Anderson Model Irreducible Vertex: Classical Waves TheWardIdentity Cancellation of the Impurity Scattering Terms Reduction to the Simplified Model Meaning of the Ward Identity Diffusion Constant Modification for Classical Waves Evaluation of the Wave Diffusion Constant Quantum Case: the Anderson Model Classical Wave Diffusion Constant Anisotropic Scattering and the Transport Mean FreePath Application: Diffusive Wave Spectroscopy The Siegert Relation Averaging Over the Diffusive Motion of Scatterers Averaging Over the Scattering Angles Diffusive Transport of Waves Boundary Conditions for Diffusive Light Flux Solutions for the Slab Geometry The Coherent Backscattering Effect Wave Diffusion versus Classical Diffusion Coherence in the Backscattering Direction Time Reversal Invariance
5 XII Contents 6.3 Angular Profile of the Coherent Backscattering Single Configuration and Configurational Averaging Counting the Scattering Paths Backscattering from a Random Half Space Features of the Coherent Backscattering Peak Backscattering from a Finite Thickness Slab Sample Size (Path Length) Dependence Effect of Absorption Renormalized Diffusion Coherent Backscattering Effect in the Diagrammatic Representation Evaluation of the Maximally Crossed Diagrams Momenta Transformations Summation of Maximally Crossed Diagrams Renormalized Diffusion Constant Sample Size and Spatial Dimensionality Dependencies ofwavediffusion Conductivity Correction Diffusion Constant Correction The Emergence of Localization Length Localization in 3D : the Ioffe Regel Criterion Localization in One Dimension: the Herbert Jones Thouless Formula Localization and Intensity Transmission Fluctuations in Intensity Transmission Randomness is not Always a Sufficient Condition for 1D Localization Localization and Eigenfunctions in 1D: the Characteristic Function Relation Between the 1D Localization Length and Density of States HJT Formula for the 1D Anderson Model HJT Formula for 1D Classical Scalar Waves High Frequency and Low Frequency Limiting Behaviors The Scaling Theory of Localization Distinguishing a Localized State from an Extended State The Scaling Argument and Spatial Dimensionality Dimensionless Conductance The Scaling Hypothesis and Its Consequences Defining the Scaling Function Scaling and the Effect of Randomness Behavior of the Scaling Function
6 Contents XIII When System Size is Less than the Localization Length Wave Transport Near the 3D Mobility Edge Anomalous Diffusion and the Minimum Metallic Conductance in 3D Scaling Behavior in the 3D Localized Regime Numerical Evaluation of the Scaling Function The Finite-Size Scaling Function Limiting Behaviors Relation to the Scaling Functions in 1D, 2D, and3d Universality and Limitations of the Scaling Theory Results Localization in 3D : Lattice vs. Continuum Implicit Assumptions of the Scaling Theory Localized States and the Approach to Localization The Self-Consistent Theory of Localization Transition to the Strong Scattering Regime Response of the Localized State at Finite Modulation Frequency Qualitative Evaluation of the Correction Term Localization Behavior of the Anderson Model Evaluation of the Maximally Crossed Diagrams Contribution Mobility Edge in 3D Anderson Model Localization Length and Correlation Length in the 3D Anderson Model D Anderson Model Localization Length in the 2D Anderson Model D Anderson Model Localization Length in the 1D Anderson Model Input Parameters to Localization Calculations Classical Scalar Wave Localization One Parameter Criterion for the Classical Wave 3D Mobility Edge Input Parameter Values and Wave Scattering Regimes Scattering and Localization of Classical Waves in 3D Periodicity in Scattering Structures and 3D Localization Localization of 2D Classical Scalar Wave Localization of 1D Classical Scalar Wave Transport Velocity of Classical Scalar Waves Transport Velocity and Scattering Resonances Effective Medium Based on Energy Homogenization
7 XIV Contents 9.5 The Scaling Function Evaluation Finite Size Modification of the Diffusion Constant Finite Size Effect for Density of States Scaling Function and its Limiting Behaviors Localization Phenomena in Electronic Systems Finite Temperatures and the Effect of Inelastic Scattering Inelastic Scattering in the Classical Wave Case Inelastic Scattering in the Electronic Case Temperature Dependence of the Resistance in 2D Disordered Films Manifestation of Localization Correction in 2D Conductivity Magnetoresistance of Disordered Metallic Films Effect of a Magnetic Field Magnetic Field Correction to the Coherent Backscattering Effect Thick Film Case Thin Film Case Diffusion and Inelastic Relaxation Magnetoresistance and the Distance to Localization Spin-Orbit Coupling Transport of Localized States at Finite Temperatures: Hopping Conduction Constructing the Critical Percolating Path ofleastresistance Temperature Dependence of the Critical Path Conductance Variable Range Hopping Mesoscopic Phenomena What is Mesoscopic? Dissipation and Mesoscopic Conductance Intensity Distribution of the Speckle Pattern Statistical Independence and Gaussian Distribution Correlations in the Diffusive Intensity Frequency Correlation of the Diffusive Intensity Spatial Correlation in the Diffusive Intensity Intensity Fluctuations for Classical Waves in 3D Long-Range Correlation in Intensity Fluctuations Reduction to a Diffusion Problem with Random Sources Solution in the Slab Geometry Slow Decay of Transmitted Intensity Fluctuations Landauer Formula and Quantized Conductance
8 Contents XV Quantized Conductance Two-Terminal versus Four-Terminal The Single Channel (1D) Case Landauer Buttiker Formula for the Multichannel Case Characteristics of Mesoscopic Conductance Disordered 2D Metallic Film Distribution of the Dimensionless Conductances Localization Length, Conductance Fluctuations and Transport Regimes Heuristic Explanation of Universal Conductance Fluctuations References Index...331
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