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

Ping Sheng (Autor)

eBook Download: PDF

1995 | 1. Auflage
339 Seiten
Elsevier Science (Verlag)
978-0-08-053506-7 (ISBN)

Infos

This book gives readers a coherent picture of waves in disordered media, including multiple scattered waves. The book is intended to be self-contained, with illustrated problems and solutions at the end of each chapter to serve the double purpose of filling out the technical and mathematical details and giving the students exercises if used as a course textbook.
The study of wave behavior in disordered media has applications in:
Condensed matter physics (semi and superconductor nanostructures and mesoscopic phenomena)
Materials science/analytical chemistry (analysis of composite and crystalline structures and properties)
Optics and electronics (microelectronic and optoelectronic devices)
Geology (seismic exploration of Earths subsurface)

Inhalt

Front Cover 1
Introduction to Wave Scattering, Localization, and Mesoscopic Phenomena 4
Copyright Page 5
Contents 6
Preface 10
Chapter 1. Introduction 14
References 27
Chapter 2. Quantum and Classical Waves 28
2.1 Preliminaries 28
2.2 Green's Functions for Waves in a Uniform Medium 32
2.3 Waves on a Discrete Lattice 39
2.4 Lattice Green's Functions 44
2.5 Treating Continuum Problems on a Lattice 50
Problems and Solutions 53
Reference 61
Chapter 3. Wave Scattering and the Effective Medium 62
3.1 An Overview of the Approach 62
3.2 Wave Scattering Formalism 64
3.3 Single Scatterer—The Lattice Case 68
3.4 Single Scatterer—The Continuum Case 71
3.5 Infinite Number of Scatterers—The Effective Medium and the Coherent Potential Approximation 79
3.6 CPA—The Anderson Model 82
3.7 CPA—The Case of Classical Waves 86
3.8 Accuracy of the CPA 97
3.9 Extension of the CPA to the Intermediate Frequency Regime 98
Problems and Solutions 100
References 126
Chapter 4. Diffusive Waves 128
4.1 Beyond the Effective Medium 128
4.2 Pulse Intensity Evolution in a Random Medium 129
4.3 The Bethe–Salpeter Equation and Its Solution by Moments 134
4.4 The Vertex Function 147
4.5 The Ward Identity 158
4.6 Modification of the Diffusion Constant Due to Frequency-Dependent Scattering Potentials 164
4.7 Evaluation of the Wave Diffusion Constant 166
4.8 Application: Diffusive Wave Spectroscopy 173
Problems and Solutions 184
References 188
Chapter 5. The Coherent Backscattering Effect 190
5.1 Wave Diffusion versus Classical Diffusion 190
5.2 Coherence in the Backscattering Direction 191
5.3 Angular Profile of the Coherent Backscattering 194
5.4 Sample Size (Path Length) Dependence 198
Problems and Solutions 202
References 205
Chapter 6. Renormalized Diffusion 206
6.1 Coherent Backscattering Effect in the Diagrammatic Representation 206
6.2 Evaluation of the Maximally Crossed Diagrams 208
6.3 Renormalized Diffusion Constant 212
6.4 Sample Size and Spatial Dimensionality Dependences of Wave Diffusion 214
6.5 Localization in One Dimension: The Herbert–Jones–Thouless Formula 216
Problems and Solutions 224
References 226
Chapter 7. The Scaling Theory of Localization 228
7.1 Distinguishing a Localized State from an Extended State 228
7.2 The Scaling Hypothesis and Its Consequences 231
7.3 Finite-Size Scaling Calculation of ß (ln .) 239
7.4 Universality and Limitations of the Scaling Theory Results 245
Problem and Solution 247
References 252
Chapter 8. Localized States and the Approach to Localization 254
8.1 The Self-Consistent Theory of Localization 254
8.2 Localization Behavior of the Anderson Model 257
8.3 Classical Scalar Wave Localization 272
8.4 Transport Velocity of Classical Scalar Waves 282
8.5 The Scaling Function ß (In .) 284
Problems and Solutions 290
References 294
Chapter 9. Localization Phenomena in Electronic Systems 296
9.1 Finite Temperatures and the Effect of Inelastic Scattering 296
9.2 Temperature Dependence of the Resistance in 2D Disordered Films 297
9.3 Magnetoresistance of Disordered Metallic Films 300
9.4 Transport of Localized States at Finite Temperatures—Hopping Conduction 306
Problems and Solutions 311
References 313
Chapter 10. Mesoscopic Phenomena 314
10.1 What is "Mesoscopic"? 314
10.2 Intensity Distribution of the Speckle Pattern 315
10.3 Correlations in the Speckle Pattern 317
10.4 Long-Range Correlation in Intensity Fluctuations 323
10.5 Landauer's Formula and Quantized Conductances 328
10.6 Characteristics of Mesoscopic Conductance 333
Problems and Solutions 338
References 340
Index 342

Produkt-Details

• Erscheint lt. Verlag: 4.4.1995
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Angewandte Physik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Festkörperphysik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Mechanik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
• Themenwelt: Technik ► Bauwesen
• Themenwelt: Technik ► Elektrotechnik / Energietechnik
• Themenwelt: Technik ► Maschinenbau
• Themenwelt: Technik ► Umwelttechnik / Biotechnologie
• Themenwelt: Wirtschaft
• ISBN-10: 0-08-053506-2 / 0080535062
• ISBN-13: 978-0-08-053506-7 / 9780080535067