Introduction to Wave Scattering, Localization and Mesoscopic Phenomena (eBook)

Preface to the Second Edition 6
Preface to the First Edition 8
Contents 10
1 Introduction 17
1.1 Relevant Length Scales 17
1.2 Diffusive Transport 18
1.3 Coherent Backscattering and the Approach to Localization 19
1.4 Sample Size Dependence 20
1.5 Localization and Scaling 22
1.6 Spatial Dimensionality in Localization and Di.usion 24
1.7 Mesoscopic Phenomena 27
1.8 Localization vs. Con.nement 29
1.9 Topics not Covered 29
2 Quantum and Classical Waves 31
2.1 Preliminaries 31
2.2 Green Functions for Waves in a Uniform Medium 34
2.3 Waves on a Discrete Lattice 40
2.4 Lattice Green Functions 45
2.5 Treating Continuum Problems on a Lattice 50
2.6 Problems and Solutions 52
3 Wave Scattering and the Coherent Potential Approximation 60
3.1 An Overview of the Approach 60
3.2 Wave Scattering Formalism 62
3.3 Single Scatterer: the Lattice Case 66
3.4 Single Scatterer: the Continuum Case 68
3.5 Infinite Number of Scatterers: the Effective Medium 75
3.6 Accuracy of the CPA 77
Problems and Solutions 78
4 Coherent Waves and E.ective Media 90
4.1 Coherence and Homogenization 90
4.2 CPA: The Anderson Model 91
4.3 CPA: The Classical Waves 95
4.4 Effective Medium Modeling of Inhomogeneous Materials 107
4.5 The Spectral Function Approach: Coherent Quasimodes 117
Problems and Solutions 131
5 Diffusive Waves 141
5.1 Beyond the Coherent Regime 141
5.2 Pulse Intensity Evolution in a Random Medium 142
5.3 The Bethe-Salpeter Equation and its Solution by Moments 145
5.4 The Vertex Function 160
5.5 The Ward Identity 169
5.6 Diffusion Constant Modi.cation for Classical Waves 174
5.7 Evaluation of the Wave Di.usion Constant 176
5.8 Application: Di.usive Wave Spectroscopy 182
6 The Coherent Backscattering E.ect 196
6.1 Wave Diffusion versus Classical Diffusion 196
6.2 Coherence in the Backscattering Direction 197
6.3 Angular Profile of the Coherent Backscattering 199
6.4 Sample Size (Path Length) Dependence 204
Problems and Solutions 207
7 Renormalized Di.usion 211
7.1 Coherent Backscattering Effect in the Diagrammatic Representation 211
7.2 Evaluation of the Maximally Crossed Diagrams 213
7.3 Renormalized Di.usion Constant 216
7.4 Sample Size and Spatial Dimensionality Dependencies of Wave Diffusion 218
7.5 Localization in One Dimension: the Herbert–Jones–Thouless Formula 220
Problems and Solutions 227
8 The Scaling Theory of Localization 230
8.1 Distinguishing a Localized State from an Extended State 230
8.2 The Scaling Hypothesis and Its Consequences 233
8.3 Numerical Evaluation of the Scaling Function 240
8.4 Universality and Limitations of the Scaling 246
Theory Results 246
9 Localized States and the Approach to Localization 253
9.1 The Self-Consistent Theory of Localization 253
9.2 Localization Behavior of the Anderson Model 256
9.3 Classical Scalar Wave Localization 267
9.4 Transport Velocity of Classical Scalar Waves 277
9.5 The Scaling Function Evaluation 280
Problems and Solutions 285
10 Localization Phenomena in Electronic Systems 290
10.1 Finite Temperatures and the Effect of Inelastic Scattering 290
10.2 Temperature Dependence of the Resistance in 2D Disordered Films 291
10.3 Magnetoresistance of Disordered Metallic Films 293
10.4 Transport of Localized States at Finite Temperatures: Hopping Conduction 299
Problems and Solutions 303
11 Mesoscopic Phenomena 306
11.1 What is “Mesoscopic”? 306
11.2 Intensity Distribution of the Speckle Pattern 307
11.3 Correlations in the Di.usive Intensity 309
11.4 Long-Range Correlation in Intensity Fluctuations 315
11.5 Landauer Formula and Quantized Conductance 319
11.6 Characteristics of Mesoscopic Conductance 324
Problems and Solutions 329
References 332
Chapter 1 332
Chapter 2 333
Chapter 3 333
Chapter 4 333
Chapter 5 334
Chapter 6 335
Chapter 7 335
Chapter 8 336
Chapter 9 337
Chapter 10 337
Chapter 11 338
Index 339