ISBN: 3-540-66566-8
TITLE: Semiclassical Theory of Mesoscopic Quantum Systems
AUTHOR: Richter, Klaus
TOC:

1. Introduction 1
1.1 A Few Examples 5
1.1.1 Antidot Superlattices 5
1.1.2 Ballistic Weak Localization in Electron Billiards 8
1.1.3 Mesoscopic Orbital Magnetism 11
1.1.4 Andreev Billiards 12
1.1.5 Quantum Corrals 13
1.2 Purpose of This Book and Overview 15
2. Elements of Modern Semiclassical Theory 19
2.1 Green Functions and Trace Formulas 19
2.1.1 Semiclassical Green Function 20
2.1.2 Density of States 24
2.1.3 BerryTabor Trace Formula 25
2.1.4 Gutzwiller Trace Formula 26
2.2 Spectral Correlations 29
2.3 Thermodynamic Quantities 32
2.4 Semiclassical Linear Response 35
2.4.1 Basic Quantum Mechanical Relations 36
2.4.2 Semiclassical Approximation: Overview 39
2.4.3 Chaotic Case 40
2.4.4 Integrable Case 45
2.4.5 Dynamic Susceptibilities 46
3. Ballistic Quantum Transport 49
3.1 Bulk Conductivity 51
3.1.1 Semiclassical Approach 51
3.1.2 Antidot Lattices: Experiments 55
3.1.3 Antidot Lattices: Conductivity Calculations 56
3.2 Transport Through Phase-Coherent Conductors 62
3.2.1 Semiclassical Approach to Landauer Conductance 63
3.2.2 Trajectory Analysis 66
3.2.3 Weak Localization 66
3.2.4 Finite Antidot Arrays 68
3.2.5 Conductance Fluctuations 71
3.3 Limitations of Present Semiclassical Transport Theory 73
4. Orbital Magnetism 79
4.1 Historical Backround and Overview 79
4.2 Basic Concepts 83
4.2.1 Definitions 83
4.2.2 Bulk Properties: De Haasvan Alphen Effect and Landau Diamagnetism 84
4.2.3 Thermodynamics in the Mesoscopic Regime 87
4.3 Chaotic Systems 90
4.3.1 Semiclassical Approaches 91
4.3.2 Persistent Currents 94
4.3.3 Magnetic Susceptibilities 99
4.3.4 Systems with Diffusive Dynamics 104
4.3.5 Relation to Experiments 104
4.4 Perturbed Integrable Systems: General Framework 105
4.4.1 Magnetic Susceptibility 107
4.4.2 Integrable Versus Chaotic Behavior 109
4.5 Perturbed Integrable Systems: Square Quantum Wells 110
4.5.1 The WeakField Density of States 111
4.5.2 Susceptibility of Individual Samples and Ensemble Averages 114
4.5.3 Bouncing-Ball Magnetism 121
4.5.4 De Haasvan Alphen-Like Oscillations 126
4.6 Systems Integrable at Arbitrary Fields: Ring Geometries 128
4.6.1 Persistent Currents 129
5. Disorder Effects 135
5.1 Characterization 135
5.2 Semiclassical Treatment of Disorder in the Ballistic Limit 138
5.2.1 The Disorder Model 138
5.2.2 Effect on the Single-Particle Green Function 139
5.2.3 Effect on the Two-Particle Green Function 143
5.3 High Landau Levels in a Smooth Disorder Potential 144
5.4 Magnetic Susceptibility of Ballistic Quantum Dots 147
5.4.1 Fixed-Size Impurity Average 147
5.4.2 Combined Impurity and Size Average 150
5.4.3 Concluding Remarks 154
5.5 From Ballistic to Diffusive Dynamics 155
5.5.1 Spectral Correlations in the Diffusive Limit 156
5.5.2 Spectral Correlations
in Disordered Nondiffusive Systems 156
5.5.3 Orbital Magnetism 161
6. Interaction Effects 167
6.1 Diagrammatic Perturbation Theory 170
6.2 Semiclassical Formalism 171
6.3 Orbital Magnetism of Interacting Diffusive Systems 173
6.3.1 Disordered Rings 174
6.3.2 Relation to Experiments
and Other Theoretical Approaches176
6.3.3 Two-Dimensional Diffusive Structures 177
6.4 Orbital Magnetism of Interacting Ballistic Quantum Dots 179
6.4.1 Ensemble of Squares 180
6.4.2 First-Order Diagonal Channel 181
6.4.3 Renormalization from Higher-Order Diagonal Contributions 182
6.4.4 Nondiagonal Channel in Regular Systems184
6.5 Comparison Between Integrable and Chaotic Structures 185
6.6 Comparison with Experiment 187
7. Concluding Remarks 189
A. Appendices 195
A.1 Trace Integrals over Semiclassical Green Functions 195
A.1.1 Auxiliary Integrals 195
A.1.2 Integrals of Products
of Two Retarded Green Functions 198
A.1.3 Integrals of Products
of a Retarded and an Advanced Green Function 199
A.2 Numerical Calculations for Susceptibilities of Square Quantum Dots 201
A.2.1 Clean Case 201
A.2.2 Weak Disorder 202
A.2.3 Thermodynamics 202
A.3 Semiclassical and Quantum Results for Bulk Mean Free Paths 203
References 206
Index 219
END
