Semiclassical Theory of Mesoscopic Quantum Systems

by Richter, Klaus; Kuhn, J.; Muller, T.; Steiner, F.; Trumper, J.; Wolfle, P.; Hohler, G.

• ISBN13: 9783540665663
• ISBN10: 3540665668
• Format: Hardcover
• Copyright: 1999-12-01
• Publisher: Springer Nature

Summary

This book describes manifestations of classical dynamics and chaos in the quantum properties of mesoscopic systems. The first part of the book deals with integrable and chaotic classical dynamics with particular emphasis on the semiclassical description of spectral correlations, thermodynamic properties and linear response functions. The main part shows applications to prominent observables in the mesoscopic context.

Table of Contents

Introduction	p. 1
A Few Examples	p. 5
Antidot Superlattices	p. 5
Ballistic Weak Localization in Electron Billiards	p. 8
Mesoscopic Orbital Magnetism	p. 11
Andreev Billiards	p. 12
Quantum Corrals	p. 13
Purpose of This Book and Overview	p. 15
Elements of Modern Semiclassical Theory	p. 19
Green Functions and Trace Formulas	p. 19
Semiclassical Green Function	p. 20
Density of States	p. 24
Berry-Tabor Trace Formula	p. 25
Gutzwiller Trace Formula	p. 26
Spectral Correlations	p. 29
Thermodynamic Quantities	p. 32
Semiclassical Linear Response	p. 35
Basic Quantum Mechanical Relations	p. 36
Semiclassical Approximation: Overview	p. 39
Chaotic Case	p. 40
Integrable Case	p. 45
Dynamic Susceptibilities	p. 46
Ballistic Quantum Transport	p. 49
Bulk Conductivity	p. 51
Semiclassical Approach	p. 51
Antidot Lattices: Experiments	p. 55
Antidot Lattices: Conductivity Calculations	p. 56
Transport Through Phase-Coherent Conductors	p. 62
Semiclassical Approach to Landauer Conductance	p. 63
Trajectory Analysis	p. 66
Weak Localization	p. 66
Finite Antidot Arrays	p. 68
Conductance Fluctuations	p. 71
Limitations of Present Semiclassical Transport Theory	p. 73
Orbital Magnetism	p. 79
Historical Backround and Overview	p. 79
Basic Concepts	p. 83
Definitions	p. 83
Bulk Properties: De Haas-van Alphen Effect and Landau Diamagnetism	p. 84
Thermodynamics in the Mesoscopic Regime	p. 87
Chaotic Systems	p. 90
Semiclassical Approaches	p. 91
Persistent Currents	p. 94
Magnetic Susceptibilities	p. 99
Systems with Diffusive Dynamics	p. 104
Relation to Experiments	p. 104
Perturbed Integrable Systems: General Framework	p. 105
Magnetic Susceptibility	p. 107
Integrable Versus Chaotic Behavior	p. 109
Perturbed Integrable Systems: Square Quantum Wells	p. 110
The Weak-Field Density of States	p. 111
Susceptibility of Individual Samples and Ensemble Averages	p. 114
Bouncing-Ball Magnetism	p. 121
De Haas-van Alphen-Like Oscillations	p. 126
Systems Integrable at Arbitrary Fields: Ring Geometries	p. 128
Persistent Currents	p. 129
Disorder Effects	p. 135
Characterization	p. 135
Semiclassical Treatment of Disorder in the Ballistic Limit	p. 138
The Disorder Model	p. 138
Effect on the Single-Particle Green Function	p. 139
Effect on the Two-Particle Green Function	p. 143
High Landau Levels in a Smooth Disorder Potential	p. 144
Magnetic Susceptibility of Ballistic Quantum Dots	p. 147
Fixed-Size Impurity Average	p. 147
Combined Impurity and Size Average	p. 150
Concluding Remarks	p. 154
From Ballistic to Diffusive Dynamics	p. 155
Spectral Correlations in the Diffusive Limit	p. 156
Spectral Correlations in Disordered Nondiffusive Systems	p. 156
Orbital Magnetism	p. 161
Interaction Effects	p. 167
Diagrammatic Perturbation Theory	p. 170
Semiclassical Formalism	p. 171
Orbital Magnetism of Interacting Diffusive Systems	p. 173
Disordered Rings	p. 174
Relation to Experiments and Other Theoretical Approaches	p. 176
Two-Dimensional Diffusive Structures	p. 177
Orbital Magnetism of Interacting Ballistic Quantum Dots	p. 179
Ensemble of Squares	p. 180
First-Order Diagonal Channel	p. 181
Renormalization from Higher-Order Diagonal Contributions	p. 182
Nondiagonal Channel in Regular Systems	p. 184
Comparison Between Integrable and Chaotic Structures	p. 185
Comparison with Experiment	p. 187
Concluding Remarks	p. 189
Appendices	p. 195
Trace Integrals over Semiclassical Green Functions	p. 195
Auxiliary Integrals	p. 195
Integrals of Products of Two Retarded Green Functions	p. 198
Integrals of Products of a Retarded and an Advanced Green Function	p. 199
Numerical Calculations for Susceptibilities of Square Quantum Dots	p. 201
Clean Case	p. 201
Weak Disorder	p. 202
Thermodynamics	p. 202
Semiclassical and Quantum Results for Bulk Mean Free Paths	p. 203
References	p. 206
Index	p. 219
Table of Contents provided by Publisher. All Rights Reserved.