Quantum and Semi-classical Percolation and Breakdown in Disordered Solids

by Sen, A. K.; Bardhan, K. K.; Chakrabarti, B. K.

• ISBN13: 9783540854272
• ISBN10: 3540854274
• Format: Hardcover
• Copyright: 2009-05-04
• Publisher: Springer Verlag

Summary

This set of extensive tutorial reviews and lectures focuses on the semi-classical and quantum aspects of percolation methods and their application to breakdown phenomena in disordered composite or granular materials. It sets out to connect - for the first time and in a coherent fashion - many recent theoretical and experimental advances in adjacent fields, such as the investigation of nonlinear current-voltage characteristics of 'quantum-dotted' materials or Zener breakdown in Mott or Anderson insulators. Last but not least, a final chapter explores the application of quantum percolation methods to the rapidly emerging field of quantum computing and communication.

Table of Contents

Classical Percolation	p. 1
Introduction	p. 1
Methods	p. 3
Quantities and Exponents	p. 6
Fractal Dimension: Incipient Infinite Cluster	p. 9
Simple Renormalisation Group	p. 12
Diffusion and Percolation	p. 14
Summary	p. 18
References	p. 18
Nonlinear Response, Semi-classical Percolation and Breakdown in the RRTN Model	p. 21
Introduction	p. 21
The Origin of the RRTN Model and Its Percolative Aspects	p. 27
Nonlinear Steady-State I-V Characteristics	p. 35
Periodic Driving and AC-Response in the RRTN/CRC Model	p. 46
VRH and Low Temperature Conduction in the RRTN	p. 55
Slow Power-law Dynamics Far-from-Equilibrium	p. 59
Aspects of Reversible Breakdown in the RRTN Model	p. 65
Dynamical Characteristics of Breakdown	p. 73
Summary and Further Works	p. 77
References	p. 78
Quantum Transmittance Through Random Media	p. 83
Introduction	p. 83
One Parameter Scaling Theory of Localization	p. 84
Transport Mechanisms in Disordered Media	p. 85
Some Models of Disordered Systems	p. 87
Some Earlier Studies on the Quantum Percolation Model	p. 89
The Vector Recursion Method and Its Applications	p. 92
Conclusions	p. 105
References	p. 106
Quantum Percolation in Two Dimensions	p. 109
Introduction	p. 109
Resonances and Phase Variations in Ordered Limit	p. 116
Time-Independent Schrodinger Equation for Finite Disorder	p. 120
Time-Dependent Schrodinger Equation: Sending a Wave Packet Through a 2D Cluster	p. 125
Summary	p. 132
References	p. 133
Quantum Percolation in Disordered Structures	p. 135
Introduction	p. 135
Local Distribution Approach	p. 137
Localization Effects in Quantum Percolation	p. 144
Percolative Effects in Advanced Materials	p. 154
Conclusions	p. 159
References	p. 160
Quantum Percolation in the Quantum Hall Regime	p. 163
Introduction	p. 163
The Quantized Hall Effect and Classical Percolation	p. 165
Network Models at the IQHE	p. 168
Hartree-Fock Approach to the IQHE	p. 184
Conclusions	p. 189
References	p. 190
Percolative Quantum Transport in Manganites	p. 195
Introduction	p. 195
Standard Quantum Percolation	p. 196
Manganites: Phenomenology and Model	p. 198
Percolative Effects in a One Band Model of Phase Competition	p. 205
Percolation in Two Band Models with Electron-Phonon Coupling	p. 217
Connection with Quantum Percolation and Resistor Networks	p. 221
Conclusions	p. 225
References	p. 225
Classical and Quantum Breakdown in Disordered Materials	p. 227
Introduction	p. 227
Analysis of the Fuse Problem	p. 229
Dielectric Breakdown Problem	p. 238
Zener Breakdown in Anderson Insulators	p. 247
Conclusions	p. 249
References	p. 249
Nonequilibrium Quantum Breakdown in a Strongly Correlated Electron System	p. 251
Introduction	p. 251
Nonadiabatic Evolution and Pair Creation of Carriers	p. 256
References	p. 283
Percolation in Quantum Computation and Communication	p. 287
Introduction	p. 287
Percolation and Quantum Computing	p. 290
Quantum Repeater Networks for Quantum Communication	p. 307
Summary and Open Problems	p. 315
References	p. 317
Index	p. 321
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