Sheng Introduction to Wave Scattering, Localization and Mesoscopic Phenomena

2. Auflage 2006
ISBN: 978-3-540-29156-5
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 88, 329 Seiten, eBook

Reihe: Springer Series in Materials Science

Waves represent a classic topic of study in physics, mathematics, and engineering. Many modern technologies are based on our understanding of waves and their interaction with matter. In the past thirty years, there have been some revolutionary developments in the study of waves. The present volume is the only available source which details these developments in a systematic manner, with the aim of reaching a broad audience of non-experts.

It is an important resource book for those interested in understanding the physics underlying nanotechnology and mesoscopic phenomena, as well as for bridging the gap between the textbooks and research frontiers in any wave related topic. A special feature of this volume is the treatment of classical and quantum mechanical waves within a unified framework, thus facilitating an understanding of similarities and differences between the two.

Zielgruppe

Research

Autoren/Hrsg.

Sheng, Ping

Inhaltsverzeichnis

1;Preface to the Second Edition;6
2;Preface to the First Edition;8
3;Contents;10
4;1 Introduction;17
4.1;1.1 Relevant Length Scales;17
4.2;1.2 Diffusive Transport;18
4.3;1.3 Coherent Backscattering and the Approach to Localization;19
4.4;1.4 Sample Size Dependence;20
4.5;1.5 Localization and Scaling;22
4.6;1.6 Spatial Dimensionality in Localization and Di.usion;24
4.7;1.7 Mesoscopic Phenomena;27
4.8;1.8 Localization vs. Con.nement;29
4.9;1.9 Topics not Covered;29
5;2 Quantum and Classical Waves;31
5.1;2.1 Preliminaries;31
5.2;2.2 Green Functions for Waves in a Uniform Medium;34
5.3;2.3 Waves on a Discrete Lattice;40
5.4;2.4 Lattice Green Functions;45
5.5;2.5 Treating Continuum Problems on a Lattice;50
5.6;2.6 Problems and Solutions;52
6;3 Wave Scattering and the Coherent Potential Approximation;60
6.1;3.1 An Overview of the Approach;60
6.2;3.2 Wave Scattering Formalism;62
6.3;3.3 Single Scatterer: the Lattice Case;66
6.4;3.4 Single Scatterer: the Continuum Case;68
6.5;3.5 Infinite Number of Scatterers: the Effective Medium;75
6.6;3.6 Accuracy of the CPA;77
6.7;Problems and Solutions;78
7;4 Coherent Waves and E.ective Media;90
7.1;4.1 Coherence and Homogenization;90
7.2;4.2 CPA: The Anderson Model;91
7.3;4.3 CPA: The Classical Waves;95
7.4;4.4 Effective Medium Modeling of Inhomogeneous Materials;107
7.5;4.5 The Spectral Function Approach: Coherent Quasimodes;117
7.6;Problems and Solutions;131
8;5 Diffusive Waves;141
8.1;5.1 Beyond the Coherent Regime;141
8.2;5.2 Pulse Intensity Evolution in a Random Medium;142
8.3;5.3 The Bethe-Salpeter Equation and its Solution by Moments;145
8.4;5.4 The Vertex Function;160
8.5;5.5 The Ward Identity;169
8.6;5.6 Diffusion Constant Modi.cation for Classical Waves;174
8.7;5.7 Evaluation of the Wave Di.usion Constant;176
8.8;5.8 Application: Di.usive Wave Spectroscopy;182
9;6 The Coherent Backscattering E.ect;196
9.1;6.1 Wave Diffusion versus Classical Diffusion;196
9.2;6.2 Coherence in the Backscattering Direction;197
9.3;6.3 Angular Profile of the Coherent Backscattering;199
9.4;6.4 Sample Size (Path Length) Dependence;204
9.5;Problems and Solutions;207
10;7 Renormalized Di.usion;211
10.1;7.1 Coherent Backscattering Effect in the Diagrammatic Representation;211
10.2;7.2 Evaluation of the Maximally Crossed Diagrams;213
10.3;7.3 Renormalized Di.usion Constant;216
10.4;7.4 Sample Size and Spatial Dimensionality Dependencies of Wave Diffusion;218
10.5;7.5 Localization in One Dimension: the Herbert–Jones–Thouless Formula;220
10.6;Problems and Solutions;227
11;8 The Scaling Theory of Localization;230
11.1;8.1 Distinguishing a Localized State from an Extended State;230
11.2;8.2 The Scaling Hypothesis and Its Consequences;233
11.3;8.3 Numerical Evaluation of the Scaling Function;240
11.4;8.4 Universality and Limitations of the Scaling;246
11.5;Theory Results;246
12;9 Localized States and the Approach to Localization;253
12.1;9.1 The Self-Consistent Theory of Localization;253
12.2;9.2 Localization Behavior of the Anderson Model;256
12.3;9.3 Classical Scalar Wave Localization;267
12.4;9.4 Transport Velocity of Classical Scalar Waves;277
12.5;9.5 The Scaling Function Evaluation;280
12.6;Problems and Solutions;285
13;10 Localization Phenomena in Electronic Systems;290
13.1;10.1 Finite Temperatures and the Effect of Inelastic Scattering;290
13.2;10.2 Temperature Dependence of the Resistance in 2D Disordered Films;291
13.3;10.3 Magnetoresistance of Disordered Metallic Films;293
13.4;10.4 Transport of Localized States at Finite Temperatures: Hopping Conduction;299
13.5;Problems and Solutions;303
14;11 Mesoscopic Phenomena;306
14.1;11.1 What is “Mesoscopic”?;306
14.2;11.2 Intensity Distribution of the Speckle Pattern;307
14.3;11.3 Correlations in the Di.usive Intensity;309
14.4;11.4 Long-Range Correlation in Intensity Fluctuations;315
14.5;11.5 Landauer Formula and Quantized Conductance;319
14.6;11.6 Characteristics of Mesoscopic Conductance;324
14.7;Problems and Solutions;329
15;References;332
15.1;Chapter 1;332
15.2;Chapter 2;333
15.3;Chapter 3;333
15.4;Chapter 4;333
15.5;Chapter 5;334
15.6;Chapter 6;335
15.7;Chapter 7;335
15.8;Chapter 8;336
15.9;Chapter 9;337
15.10;Chapter 10;337
15.11;Chapter 11;338
16;Index;339

Quantum and Classical Waves.- Wave Scattering and the Coherent Potential Approximation.- Coherent Waves and Effective Media.- Diffusive Waves.- The Coherent Backscattering Effect.- Renormalized Diffusion.- The Scaling Theory of Localization.- Localized States and the Approach to Localization.- Localization Phenomena in Electronic Systems.- Mesoscopic Phenomena.