Introduction to wave scattering, localization, and mesoscopic phenomena:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2006
|
| Edition: | 2.ed. |
| Series: | Springer series in materials science
88 |
| Subjects: | |
| Online Access: | Beschreibung für Leser http://deposit.dnb.de/cgi-bin/dokserv?id=2681084&prov=M&dok\0331var=1&dok\0331ext=htm Inhaltsverzeichnis |
| Item Description: | Literaturangaben S. [323] - 329 |
| Physical Description: | XV, 333 S. graph. Darst. |
| ISBN: | 3540291555 9783540291558 |
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| 100 | 1 | |a Sheng, Ping |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Introduction to wave scattering, localization, and mesoscopic phenomena |c P. Sheng |
| 250 | |a 2.ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2006 | |
| 300 | |a XV, 333 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Springer series in materials science |v 88 | |
| 500 | |a Literaturangaben S. [323] - 329 | ||
| 650 | 4 | |a Localization theory | |
| 650 | 4 | |a Scattering (Physics) | |
| 650 | 4 | |a Waves | |
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| 650 | 0 | 7 | |a Lokalisationstheorie |0 (DE-588)4203492-9 |2 gnd |9 rswk-swf |
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| adam_text | Contents
1
Introduction
............................................... 1
1.1 Relevant
Length Scales
................................... 1
1.2
Diffusive Transport
...................................... 2
1.3
Coherent Backscattering and the Approach to Localization
... 3
1.4
Sample Size Dependence
................................. 4
1.5
Localization and Scaling
.................................. 6
1.6
Spatial Dimensionality in Localization and Diffusion
......... 8
1.7
Mesoscopic Phenomena
.................................. 11
1.8
Localization vs. Confinement
.............................. 13
1.9
Topics not Covered
...................................... 13
2
Quantum and Classical Waves
............................. 15
2.1
Preliminaries
............................................ 15
2.1.1
Quantum and Classical Wave Equations
.............. 16
2.2
Green Functions for Waves in a Uniform Medium
............ 18
2.2.1
Green Function for the Uniform Medium
............. 19
2.2.2
Green Function and the Density of States
............ 21
2.2.3
Real Space Green Functions
........................ 23
2.3
Waves on a Discrete Lattice
.............................. 24
2.3.1
Dispersion Relation
................................ 24
2.3.2
Random Discrete Lattices: the Anderson Model
....... 28
2.4
Lattice Green Functions
.................................. 29
2.4.1
ID Lattice Green Function
......................... 30
2.4.2
2D Lattice Green Function
......................... 32
2.4.3 3D
Lattice Green Function
......................... 33
2.5
Treating Continuum Problems on a Lattice
................. 34
2.6
Problems and Solutions
.................................. 36
3
Wave Scattering and the Coherent
Potential Approximation
.................................. 45
3.1
An Overview of the Approach
............................. 45
X
Contents
3.1.1 Information
from the First Moment
.................. 46
3.1.2
Information from the Second Moment
................ 46
3.1.3
Information from Higher Moments
................... 46
3.2
Wave Scattering Formalism
............................... 47
3.2.1
The Operator Notation
............................ 48
3.2.2
The
Τ
Operator
................................... 49
3.2.3
Configurational Averaging
.......................... 50
3.2.4
The Self-Energy
................................... 50
3.3
Single Scatterer: the Lattice Case
.......................... 51
3.3.1
Impurity Bound State
.............................. 52
3.4
Single Scatterer: the Continuum Case
...................... 53
3.4.1
Wave Function in the Single Scatterer Case
........... 55
3.4.2
A Digression on Notation
........................... 55
3.4.3
Scattering Amplitude and the
t
Operator
............. 56
3.4.4
Scattering Amplitude and the Optical Theorem:
3D
Case
.......................................... 57
3.4.5
Scattering Amplitude and the Optical Theorem:
2DCase
.......................................... 58
3.4.6
Scattering Amplitude and the Optical Theorem:
ID Case
.......................................... 59
3.5
Infinite Number of Scatterers: the Effective Medium
......... 60
3.5.1
Meaning of a k-Independent Self Energy
.............. 60
3.5.2
The Mean Free Path
............................... 60
3.5.3
The Coherent Potential Approximation
(СРА)
........ 61
3.6
Accuracy of the
СРА
.................................... 62
4
Coherent Waves and Effective Media
...................... 75
4.1
Coherence and Homogenization
........................... 75
4.2
СРА:
The Anderson Model
............................... 76
4.2.1
Efficient Green Function Evaluation from DOS
........ 78
4.3
СРА:
The Classical Waves
................................ 80
4.3.1
The Role of
Microstructure
......................... 81
4.3.2
The Symmetric
Microstructure
...................... 83
4.3.3
The Dispersion
Microstructure
...................... 88
4.4
Effective Medium Modeling of Inhomogeneous Materials
...... 92
4.4.1
Granular Metals
................................... 92
4.4.2
Sedimentary Rocks
................................ 94
4.5
The Spectral Function Approach: Coherent Quasimodes
......102
4.5.1
Formulation
......................................104
4.5.2
Coherent Acoustic Waves in the Intermediate
Wavelength Regime
................................106
4.5.3
Novel Acoustic Modes in Colloidal Suspensions
........108
4.5.4
Group Velocity in Strongly Scattering Media
..........112
4.5.5
Accuracy of the Spectral Function Approach
..........116
Contents
XI
Diffusive Waves
............................................127
5.1
Beyond the Coherent Regime
.............................127
5.2
Pulse Intensity Evolution in a Random Medium
.............128
5.3
The Bethe-Salpeter Equation and its Solution by Moments
.. . 131
5.3.1
Notations
........................................132
5.3.2
Irreducible Vertex Function and the Bethe-
Salpeter Equation
.................................134
5.3.3
Diffusive Behavior from a Simplified Model
...........136
5.3.4
The Ward Identity in the Simplified Model
...........137
5.3.5
Formal Derivation of the Diffusive Pole
and the Diffusion Constant
.........................139
5.3.6
Higher Moment of the Transport Equation
...........140
5.3.7
Expansion of
ф^
...................................141
5.3.8
Solution for the Diffusive Pole and the Diffusion
Constant
.........................................143
5.3.9
Configurational Averaging and Dissipation
............145
5.4
The Vertex Function
.....................................146
5.4.1
The Reducible Vertex and Diagrammatic
Representations
...................................146
5.4.2
СРА
for
Г:
the Ladder Diagrams
and the Irreducible Vertex
..........................147
5.4.3
Irreducible Vertex: the Anderson Model
..............150
5.4.4
Irreducible Vertex: Classical Waves
..................152
5.5
The Ward Identity
.......................................155
5.5.1
Cancellation of the Impurity Scattering Terms
........157
5.5.2
Reduction to the Simplified Model
...................159
5.5.3
Meaning of the Ward Identity
.......................160
5.6
Diffusion Constant Modification for Classical Waves
.........160
5.7
Evaluation of the Wave Diffusion Constant
.................162
5.7.1
Quantum Case: the Anderson Model
.................162
5.7.2
Classical Wave Diffusion Constant
...................165
5.7.3 Anisotropie
Scattering and the Transport Mean
Free Path
........................................167
5.8
Application: Diffusive Wave Spectroscopy
...................168
5.8.1
The Siegert Relation
...............................168
5.8.2
Averaging Over the Diffusive Motion of Scatterers
.....170
5.8.3
Averaging Over the Scattering Angles
................170
5.8.4
Diffusive Transport of Waves
.......................171
5.8.5
Boundary Conditions for Diffusive Light Flux
.........173
5.8.6
Solutions for the Slab Geometry
.....................174
The Coherent Backscattering Effect
.......................183
6.1
Wave Diffusion versus Classical Diffusion
...................183
6.2
Coherence in the Backscattering Direction
..................184
6.2.1
Time Reversal
Invariance
...........................185
XII Contents
6.3
Angular
Profile
of the Coherent Backscattering
..............186
6.3.1
Single Configuration and Configurational Averaging
... 187
6.3.2
Counting the Scattering Paths
......................188
6.3.3
Backscattering from a Random Half Space
............188
6.3.4
Features of the Coherent Backscattering Peak
.........189
6.3.5
Backscattering from a Finite Thickness Slab
..........190
6.4
Sample Size (Path Length) Dependence
....................191
6.4.1
Effect of Absorption
...............................194
7
Renormalized Diffusion
....................................199
7.1
Coherent Backscattering Effect in the Diagrammatic
Representation
..........................................199
7.2
Evaluation of the Maximally Crossed Diagrams
.............201
7.2.1
Momenta Transformations
..........................201
7.2.2
Summation of Maximally Crossed Diagrams
..........203
7.3
Renormalized Diffusion Constant
..........................204
7.4
Sample Size and Spatial Dimensionality Dependencies
of Wave Diffusion
........................................206
7.4.1
Conductivity Correction
............................206
7.4.2
Diffusion Constant Correction
.......................206
7.4.3
The Emergence of Localization Length
...............207
7.4.4
Localization in
3D :
the Ioffe
- Regel
Criterion
........207
7.5
Localization in One Dimension:
the Herbert-Jones-Thouless Formula
......................208
7.5.1
Localization and Intensity Transmission
..............208
7.5.2
Fluctuations in Intensity Transmission
...............209
7.5.3
Randomness is not Always a Sufficient Condition
for ID Localization
................................210
7.5.4
Localization and Eigenfunctions in ID:
the Characteristic Function
.........................210
7.5.5
Relation Between the ID Localization Length
and Density of States
..............................211
7.5.6
HJT Formula for the ID Anderson Model
............212
7.5.7
HJT Formula for ID Classical Scalar Waves
..........212
7.5.8
High Frequency and Low Frequency Limiting
Behaviors
........................................214
8
The Scaling Theory of Localization
........................219
8.1
Distinguishing a Localized State from an Extended State
.....219
8.1.1
The Scaling Argument and Spatial Dimensionality
.....220
8.1.2
Dimensionless Conductance
.........................221
8.2
The Scaling Hypothesis and Its Consequences
...............222
8.2.1
Defining the Scaling Function
.......................223
8.2.2
Scaling and the Effect of Randomness
................223
8.2.3
Behavior of the Scaling Function
....................224
Contents XIII
8.2.4
When System Size is Less than the Localization
Length
...........................................225
8.2.5
Wave Transport Near the
3D
Mobility Edge
..........226
8.2.6
Anomalous Diffusion and the Minimum Metallic
Conductance in
3D................................227
8.2.7
Scaling Behavior in the
3D
Localized Regime
.........228
8.3
Numerical Evaluation of the Scaling Function
...............229
8.3.1
The Finite-Size Scaling Function
....................230
8.3.2
Limiting Behaviors
................................230
8.3.3
Relation to the Scaling Functions in ID, 2D,
and
3D ..........................................231
8.4
Universality and Limitations of the Scaling Theory Results
.. . 235
8.4.1
Localization in
3D :
Lattice vs. Continuum
...........236
8.4.2
Implicit Assumptions of the Scaling Theory
...........236
Localized States and the Approach to Localization
.........243
9.1
The Self-Consistent Theory of Localization
.................243
9.1.1
Transition to the Strong Scattering Regime
...........243
9.1.2
Response of the Localized State at Finite
Modulation Frequency
.............................244
9.1.3
Qualitative Evaluation of the Correction Term
........245
9.2
Localization Behavior of the Anderson Model
...............246
9.2.1
Evaluation of the Maximally Crossed
Diagrams Contribution
............................247
9.2.2
Mobility Edge in
3D
Anderson Model
................249
9.2.3
Localization Length and Correlation Length
in the
3D
Anderson Model
..........................251
9.2.4
2D Anderson Model
...............................252
9.2.5
Localization Length in the 2D Anderson Model
.......254
9.2.6
ID Anderson Model
...............................256
9.2.7
Localization Length in the ID Anderson Model
.......257
9.2.8
Input Parameters to Localization Calculations
........257
9.3
Classical Scalar Wave Localization
.........................257
9.3.1
One Parameter Criterion for the Classical Wave
3D
Mobility Edge
.................................259
9.3.2
Input Parameter Values and Wave Scattering
Regimes
..........................................261
9.3.3
Scattering and Localization of Classical Waves in
3D... 262
9.3.4
Periodicity in Scattering Structures and
3D
Localization
......................................263
9.3.5
Localization of 2D Classical Scalar Wave
.............265
9.3.6
Localization of ID Classical Scalar Wave
.............266
9.4
Transport Velocity of Classical Scalar Waves
................267
9.4.1
Transport Velocity and Scattering Resonances
........268
9.4.2
Effective Medium Based on Energy Homogenization
... 268
XIV Contents
9.5
The Scaling Function Evaluation
..........................270
9.5.1
Finite Size Modification of the Diffusion Constant
.....271
9.5.2
Finite Size Effect for Density of States
...............271
9.5.3
Scaling Function and its Limiting Behaviors
..........273
10
Localization Phenomena in Electronic Systems
............281
10.1
Finite Temperatures and the Effect of Inelastic Scattering
.... 281
10.1.1
Inelastic Scattering in the Classical Wave Case
........281
10.1.2
Inelastic Scattering in the Electronic Case
............282
10.2
Temperature Dependence of the Resistance
in 2D Disordered Films
..................................282
10.2.1
Manifestation of Localization Correction
in 2D Conductivity
................................283
10.3 Magnetoresistance
of Disordered Metallic Films
.............284
10.3.1
Effect of a Magnetic Field
..........................285
10.3.2
Magnetic Field Correction to the Coherent
Backscattering Effect
..............................286
10.3.3
Thick Film Case
..................................286
10.3.4
Thin Film Case
...................................287
10.3.5
Diffusion and Inelastic Relaxation
...................287
10.3.6 Magnetoresistance
and the Distance to Localization.
. .. 288
10.3.7
Spin-Orbit Coupling
...............................289
10.4
Transport of Localized States at Finite Temperatures:
Hopping Conduction
.....................................290
10.4.1
Constructing the Critical Percolating Path
of Least Resistance
................................291
10.4.2
Temperature Dependence of the Critical
Path Conductance
.................................292
10.4.3
Variable Range Hopping
...........................293
11
Mesoscopic Phenomena
....................................297
11.1
What is Mesoscopic ?
...................................297
11.1.1
Dissipation and Mesoscopic Conductance
.............297
11.2
Intensity Distribution of the Speckle Pattern
................298
11.2.1
Statistical Independence and Gaussian Distribution
.... 299
11.3
Correlations in the Diffusive Intensity
......................300
11.3.1
Frequency Correlation of the Diffusive Intensity
.......301
11.3.2
Spatial Correlation in the Diffusive Intensity
..........302
11.3.3
Intensity Fluctuations for Classical Waves in
3D.......304
11.4
Long-Range Correlation in Intensity Fluctuations
............306
11.4.1
Reduction to a Diffusion Problem
with Random Sources
..............................306
11.4.2
Solution in the Slab Geometry
......................307
11.4.3
Slow Decay of Transmitted Intensity Fluctuations
.....309
11.5 Landauer
Formula and Quantized Conductance
.............310
Contents
XV
11.5.1
Quantized Conductance
............................311
11.5.2
Two-Terminal versus Four-Terminal
.................311
11.5.3
The Single Channel (ID) Case
......................312
11.5.4
Landauer-Buttiker Formula
for the Multichannel Case
..........................314
11.6
Characteristics of Mesoscopic Conductance
.................315
11.6.1
Disordered 2D Metallic Film
........................315
11.6.2
Distribution of the Dimensionless Conductances
.......316
11.6.3
Localization Length, Conductance Fluctuations
and Transport Regimes
............................317
11.6.4
Heuristic Explanation of Universal
Conductance Fluctuations
..........................319
References
.....................................................323
Index
..........................................................331
|
| adam_txt |
Contents
1
Introduction
. 1
1.1 Relevant
Length Scales
. 1
1.2
Diffusive Transport
. 2
1.3
Coherent Backscattering and the Approach to Localization
. 3
1.4
Sample Size Dependence
. 4
1.5
Localization and Scaling
. 6
1.6
Spatial Dimensionality in Localization and Diffusion
. 8
1.7
Mesoscopic Phenomena
. 11
1.8
Localization vs. Confinement
. 13
1.9
Topics not Covered
. 13
2
Quantum and Classical Waves
. 15
2.1
Preliminaries
. 15
2.1.1
Quantum and Classical Wave Equations
. 16
2.2
Green Functions for Waves in a Uniform Medium
. 18
2.2.1
Green Function for the Uniform Medium
. 19
2.2.2
Green Function and the Density of States
. 21
2.2.3
Real Space Green Functions
. 23
2.3
Waves on a Discrete Lattice
. 24
2.3.1
Dispersion Relation
. 24
2.3.2
Random Discrete Lattices: the Anderson Model
. 28
2.4
Lattice Green Functions
. 29
2.4.1
ID Lattice Green Function
. 30
2.4.2
2D Lattice Green Function
. 32
2.4.3 3D
Lattice Green Function
. 33
2.5
Treating Continuum Problems on a Lattice
. 34
2.6
Problems and Solutions
. 36
3
Wave Scattering and the Coherent
Potential Approximation
. 45
3.1
An Overview of the Approach
. 45
X
Contents
3.1.1 Information
from the First Moment
. 46
3.1.2
Information from the Second Moment
. 46
3.1.3
Information from Higher Moments
. 46
3.2
Wave Scattering Formalism
. 47
3.2.1
The Operator Notation
. 48
3.2.2
The
Τ
Operator
. 49
3.2.3
Configurational Averaging
. 50
3.2.4
The Self-Energy
. 50
3.3
Single Scatterer: the Lattice Case
. 51
3.3.1
Impurity Bound State
. 52
3.4
Single Scatterer: the Continuum Case
. 53
3.4.1
Wave Function in the Single Scatterer Case
. 55
3.4.2
A Digression on Notation
. 55
3.4.3
Scattering Amplitude and the
t
Operator
. 56
3.4.4
Scattering Amplitude and the Optical Theorem:
3D
Case
. 57
3.4.5
Scattering Amplitude and the Optical Theorem:
2DCase
. 58
3.4.6
Scattering Amplitude and the Optical Theorem:
ID Case
. 59
3.5
Infinite Number of Scatterers: the Effective Medium
. 60
3.5.1
Meaning of a k-Independent Self Energy
. 60
3.5.2
The Mean Free Path
. 60
3.5.3
The Coherent Potential Approximation
(СРА)
. 61
3.6
Accuracy of the
СРА
. 62
4
Coherent Waves and Effective Media
. 75
4.1
Coherence and Homogenization
. 75
4.2
СРА:
The Anderson Model
. 76
4.2.1
Efficient Green Function Evaluation from DOS
. 78
4.3
СРА:
The Classical Waves
. 80
4.3.1
The Role of
Microstructure
. 81
4.3.2
The Symmetric
Microstructure
. 83
4.3.3
The Dispersion
Microstructure
. 88
4.4
Effective Medium Modeling of Inhomogeneous Materials
. 92
4.4.1
Granular Metals
. 92
4.4.2
Sedimentary Rocks
. 94
4.5
The Spectral Function Approach: Coherent Quasimodes
.102
4.5.1
Formulation
.104
4.5.2
Coherent Acoustic Waves in the Intermediate
Wavelength Regime
.106
4.5.3
Novel Acoustic Modes in Colloidal Suspensions
.108
4.5.4
Group Velocity in Strongly Scattering Media
.112
4.5.5
Accuracy of the Spectral Function Approach
.116
Contents
XI
Diffusive Waves
.127
5.1
Beyond the Coherent Regime
.127
5.2
Pulse Intensity Evolution in a Random Medium
.128
5.3
The Bethe-Salpeter Equation and its Solution by Moments
. . 131
5.3.1
Notations
.132
5.3.2
Irreducible Vertex Function and the Bethe-
Salpeter Equation
.134
5.3.3
Diffusive Behavior from a Simplified Model
.136
5.3.4
The Ward Identity in the Simplified Model
.137
5.3.5
Formal Derivation of the Diffusive Pole
and the Diffusion Constant
.139
5.3.6
Higher Moment of the Transport Equation
.140
5.3.7
Expansion of
ф^
.141
5.3.8
Solution for the Diffusive Pole and the Diffusion
Constant
.143
5.3.9
Configurational Averaging and Dissipation
.145
5.4
The Vertex Function
.146
5.4.1
The Reducible Vertex and Diagrammatic
Representations
.146
5.4.2
СРА
for
Г:
the Ladder Diagrams
and the Irreducible Vertex
.147
5.4.3
Irreducible Vertex: the Anderson Model
.150
5.4.4
Irreducible Vertex: Classical Waves
.152
5.5
The Ward Identity
.155
5.5.1
Cancellation of the Impurity Scattering Terms
.157
5.5.2
Reduction to the Simplified Model
.159
5.5.3
Meaning of the Ward Identity
.160
5.6
Diffusion Constant Modification for Classical Waves
.160
5.7
Evaluation of the Wave Diffusion Constant
.162
5.7.1
Quantum Case: the Anderson Model
.162
5.7.2
Classical Wave Diffusion Constant
.165
5.7.3 Anisotropie
Scattering and the Transport Mean
Free Path
.167
5.8
Application: Diffusive Wave Spectroscopy
.168
5.8.1
The Siegert Relation
.168
5.8.2
Averaging Over the Diffusive Motion of Scatterers
.170
5.8.3
Averaging Over the Scattering Angles
.170
5.8.4
Diffusive Transport of Waves
.171
5.8.5
Boundary Conditions for Diffusive Light Flux
.173
5.8.6
Solutions for the Slab Geometry
.174
The Coherent Backscattering Effect
.183
6.1
Wave Diffusion versus Classical Diffusion
.183
6.2
Coherence in the Backscattering Direction
.184
6.2.1
Time Reversal
Invariance
.185
XII Contents
6.3
Angular
Profile
of the Coherent Backscattering
.186
6.3.1
Single Configuration and Configurational Averaging
. 187
6.3.2
Counting the Scattering Paths
.188
6.3.3
Backscattering from a Random Half Space
.188
6.3.4
Features of the Coherent Backscattering Peak
.189
6.3.5
Backscattering from a Finite Thickness Slab
.190
6.4
Sample Size (Path Length) Dependence
.191
6.4.1
Effect of Absorption
.194
7
Renormalized Diffusion
.199
7.1
Coherent Backscattering Effect in the Diagrammatic
Representation
.199
7.2
Evaluation of the Maximally Crossed Diagrams
.201
7.2.1
Momenta Transformations
.201
7.2.2
Summation of Maximally Crossed Diagrams
.203
7.3
Renormalized Diffusion Constant
.204
7.4
Sample Size and Spatial Dimensionality Dependencies
of Wave Diffusion
.206
7.4.1
Conductivity Correction
.206
7.4.2
Diffusion Constant Correction
.206
7.4.3
The Emergence of Localization Length
.207
7.4.4
Localization in
3D :
the Ioffe
- Regel
Criterion
.207
7.5
Localization in One Dimension:
the Herbert-Jones-Thouless Formula
.208
7.5.1
Localization and Intensity Transmission
.208
7.5.2
Fluctuations in Intensity Transmission
.209
7.5.3
Randomness is not Always a Sufficient Condition
for ID Localization
.210
7.5.4
Localization and Eigenfunctions in ID:
the Characteristic Function
.210
7.5.5
Relation Between the ID Localization Length
and Density of States
.211
7.5.6
HJT Formula for the ID Anderson Model
.212
7.5.7
HJT Formula for ID Classical Scalar Waves
.212
7.5.8
High Frequency and Low Frequency Limiting
Behaviors
.214
8
The Scaling Theory of Localization
.219
8.1
Distinguishing a Localized State from an Extended State
.219
8.1.1
The Scaling Argument and Spatial Dimensionality
.220
8.1.2
Dimensionless Conductance
.221
8.2
The Scaling Hypothesis and Its Consequences
.222
8.2.1
Defining the Scaling Function
.223
8.2.2
Scaling and the Effect of Randomness
.223
8.2.3
Behavior of the Scaling Function
.224
Contents XIII
8.2.4
When System Size is Less than the Localization
Length
.225
8.2.5
Wave Transport Near the
3D
Mobility Edge
.226
8.2.6
Anomalous Diffusion and the Minimum Metallic
Conductance in
3D.227
8.2.7
Scaling Behavior in the
3D
Localized Regime
.228
8.3
Numerical Evaluation of the Scaling Function
.229
8.3.1
The Finite-Size Scaling Function
.230
8.3.2
Limiting Behaviors
.230
8.3.3
Relation to the Scaling Functions in ID, 2D,
and
3D .231
8.4
Universality and Limitations of the Scaling Theory Results
. . 235
8.4.1
Localization in
3D :
Lattice vs. Continuum
.236
8.4.2
Implicit Assumptions of the Scaling Theory
.236
Localized States and the Approach to Localization
.243
9.1
The Self-Consistent Theory of Localization
.243
9.1.1
Transition to the Strong Scattering Regime
.243
9.1.2
Response of the Localized State at Finite
Modulation Frequency
.244
9.1.3
Qualitative Evaluation of the Correction Term
.245
9.2
Localization Behavior of the Anderson Model
.246
9.2.1
Evaluation of the Maximally Crossed
Diagrams' Contribution
.247
9.2.2
Mobility Edge in
3D
Anderson Model
.249
9.2.3
Localization Length and Correlation Length
in the
3D
Anderson Model
.251
9.2.4
2D Anderson Model
.252
9.2.5
Localization Length in the 2D Anderson Model
.254
9.2.6
ID Anderson Model
.256
9.2.7
Localization Length in the ID Anderson Model
.257
9.2.8
Input Parameters to Localization Calculations
.257
9.3
Classical Scalar Wave Localization
.257
9.3.1
One Parameter Criterion for the Classical Wave
3D
Mobility Edge
.259
9.3.2
Input Parameter Values and Wave Scattering
Regimes
.261
9.3.3
Scattering and Localization of Classical Waves in
3D. 262
9.3.4
Periodicity in Scattering Structures and
3D
Localization
.263
9.3.5
Localization of 2D Classical Scalar Wave
.265
9.3.6
Localization of ID Classical Scalar Wave
.266
9.4
Transport Velocity of Classical Scalar Waves
.267
9.4.1
Transport Velocity and Scattering Resonances
.268
9.4.2
Effective Medium Based on Energy Homogenization
. 268
XIV Contents
9.5
The Scaling Function Evaluation
.270
9.5.1
Finite Size Modification of the Diffusion Constant
.271
9.5.2
Finite Size Effect for Density of States
.271
9.5.3
Scaling Function and its Limiting Behaviors
.273
10
Localization Phenomena in Electronic Systems
.281
10.1
Finite Temperatures and the Effect of Inelastic Scattering
. 281
10.1.1
Inelastic Scattering in the Classical Wave Case
.281
10.1.2
Inelastic Scattering in the Electronic Case
.282
10.2
Temperature Dependence of the Resistance
in 2D Disordered Films
.282
10.2.1
Manifestation of Localization Correction
in 2D Conductivity
.283
10.3 Magnetoresistance
of Disordered Metallic Films
.284
10.3.1
Effect of a Magnetic Field
.285
10.3.2
Magnetic Field Correction to the Coherent
Backscattering Effect
.286
10.3.3
Thick Film Case
.286
10.3.4
Thin Film Case
.287
10.3.5
Diffusion and Inelastic Relaxation
.287
10.3.6 Magnetoresistance
and the Distance to Localization.
. . 288
10.3.7
Spin-Orbit Coupling
.289
10.4
Transport of Localized States at Finite Temperatures:
Hopping Conduction
.290
10.4.1
Constructing the Critical Percolating Path
of Least Resistance
.291
10.4.2
Temperature Dependence of the Critical
Path Conductance
.292
10.4.3
Variable Range Hopping
.293
11
Mesoscopic Phenomena
.297
11.1
What is "Mesoscopic"?
.297
11.1.1
Dissipation and Mesoscopic Conductance
.297
11.2
Intensity Distribution of the Speckle Pattern
.298
11.2.1
Statistical Independence and Gaussian Distribution
. 299
11.3
Correlations in the Diffusive Intensity
.300
11.3.1
Frequency Correlation of the Diffusive Intensity
.301
11.3.2
Spatial Correlation in the Diffusive Intensity
.302
11.3.3
Intensity Fluctuations for Classical Waves in
3D.304
11.4
Long-Range Correlation in Intensity Fluctuations
.306
11.4.1
Reduction to a Diffusion Problem
with Random Sources
.306
11.4.2
Solution in the Slab Geometry
.307
11.4.3
Slow Decay of Transmitted Intensity Fluctuations
.309
11.5 Landauer
Formula and Quantized Conductance
.310
Contents
XV
11.5.1
Quantized Conductance
.311
11.5.2
Two-Terminal versus Four-Terminal
.311
11.5.3
The Single Channel (ID) Case
.312
11.5.4
Landauer-Buttiker Formula
for the Multichannel Case
.314
11.6
Characteristics of Mesoscopic Conductance
.315
11.6.1
Disordered 2D Metallic Film
.315
11.6.2
Distribution of the Dimensionless Conductances
.316
11.6.3
Localization Length, Conductance Fluctuations
and Transport Regimes
.317
11.6.4
Heuristic Explanation of Universal
Conductance Fluctuations
.319
References
.323
Index
.331 |
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| author | Sheng, Ping |
| author_facet | Sheng, Ping |
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| dewey-search | 531.1133 |
| dewey-sort | 3531.1133 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| discipline_str_mv | Physik |
| edition | 2.ed. |
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| id | DE-604.BV021598867 |
| illustrated | Illustrated |
| index_date | 2024-07-02T14:46:58Z |
| indexdate | 2024-07-09T20:39:35Z |
| institution | BVB |
| isbn | 3540291555 9783540291558 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014814235 |
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| physical | XV, 333 S. graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
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| publisher | Springer |
| record_format | marc |
| series | Springer series in materials science |
| series2 | Springer series in materials science |
| spelling | Sheng, Ping Verfasser aut Introduction to wave scattering, localization, and mesoscopic phenomena P. Sheng 2.ed. Berlin [u.a.] Springer 2006 XV, 333 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer series in materials science 88 Literaturangaben S. [323] - 329 Localization theory Scattering (Physics) Waves Wellenausbreitung (DE-588)4121912-0 gnd rswk-swf Lokalisationstheorie (DE-588)4203492-9 gnd rswk-swf Ungeordnetes System (DE-588)4124353-5 gnd rswk-swf Ungeordnetes System (DE-588)4124353-5 s Wellenausbreitung (DE-588)4121912-0 s DE-604 Lokalisationstheorie (DE-588)4203492-9 s Springer series in materials science 88 (DE-604)BV000683335 88 http://deposit.dnb.de/cgi-bin/dokserv?id=2681084&prov=M&dok_var=1&dok_ext=htm Beschreibung für Leser http://deposit.dnb.de/cgi-bin/dokserv?id=2681084&prov=M&dok\0331var=1&dok\0331ext=htm Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014814235&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sheng, Ping Introduction to wave scattering, localization, and mesoscopic phenomena Springer series in materials science Localization theory Scattering (Physics) Waves Wellenausbreitung (DE-588)4121912-0 gnd Lokalisationstheorie (DE-588)4203492-9 gnd Ungeordnetes System (DE-588)4124353-5 gnd |
| subject_GND | (DE-588)4121912-0 (DE-588)4203492-9 (DE-588)4124353-5 |
| title | Introduction to wave scattering, localization, and mesoscopic phenomena |
| title_auth | Introduction to wave scattering, localization, and mesoscopic phenomena |
| title_exact_search | Introduction to wave scattering, localization, and mesoscopic phenomena |
| title_exact_search_txtP | Introduction to wave scattering, localization, and mesoscopic phenomena |
| title_full | Introduction to wave scattering, localization, and mesoscopic phenomena P. Sheng |
| title_fullStr | Introduction to wave scattering, localization, and mesoscopic phenomena P. Sheng |
| title_full_unstemmed | Introduction to wave scattering, localization, and mesoscopic phenomena P. Sheng |
| title_short | Introduction to wave scattering, localization, and mesoscopic phenomena |
| title_sort | introduction to wave scattering localization and mesoscopic phenomena |
| topic | Localization theory Scattering (Physics) Waves Wellenausbreitung (DE-588)4121912-0 gnd Lokalisationstheorie (DE-588)4203492-9 gnd Ungeordnetes System (DE-588)4124353-5 gnd |
| topic_facet | Localization theory Scattering (Physics) Waves Wellenausbreitung Lokalisationstheorie Ungeordnetes System |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=2681084&prov=M&dok_var=1&dok_ext=htm http://deposit.dnb.de/cgi-bin/dokserv?id=2681084&prov=M&dok\0331var=1&dok\0331ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014814235&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000683335 |
| work_keys_str_mv | AT shengping introductiontowavescatteringlocalizationandmesoscopicphenomena |