Quantum and Semi-classical Percolation and Breakdown in Disordered Solids Book

Classical Percolation D. Stauffer 1

1 Introduction 1

2 Methods 3

3 Quantities and Exponents 6

4 Fractal Dimension: Incipient Infinite Cluster 9

5 Simple Renormalisation Group 12

6 Diffusion and Percolation 14

7 Summary 18

References 18

Nonlinear Response, Semi-classical Percolation and Breakdown in the RRTN Model A.K. Sen 21

1 Introduction 21

2 The Origin of the RRTN Model and Its Percolative Aspects 27

3 Nonlinear Steady-State I-V Characteristics 35

4 Periodic Driving and AC-Response in the RRTN/CRC Model 46

5 VRH and Low Temperature Conduction in the RRTN 55

6 Slow Power-law Dynamics Far-from-Equilibrium 59

7 Aspects of Reversible Breakdown in the RRTN Model 65

8 Dynamical Characteristics of Breakdown 73

9 Summary and Further Works 77

References 78

Quantum Transmittance Through Random Media A. Mookerjee T. Saha-Dasgupta I. Dasgupta 83

1 Introduction 83

2 One Parameter Scaling Theory of Localization 84

3 Transport Mechanisms in Disordered Media 85

4 Some Models of Disordered Systems 87

5 Some Earlier Studies on the Quantum Percolation Model 89

6 The Vector Recursion Method and Its Applications 92

7 Conclusions 105

References 106

Quantum Percolation in Two Dimensions H. Nakanishi Md. Fhokrul Islam 109

1 Introduction 109

2 Resonances and Phase Variations in Ordered Limit 116

3 Time-Independent Schrodinger Equation for Finite Disorder 120

4 Time-Dependent Schrodinger Equation: Sending a Wave Packet Through a 2D Cluster 125

5 Summary 132

References 133

Quantum Percolation in Disordered Structures G. Schubert H. Fehske 135

1 Introduction 135

2 Local Distribution Approach 137

3 Localization Effects in QuantumPercolation 144

4 Percolative Effects in Advanced Materials 154

5 Conclusions 159

References 160

Quantum Percolation in the Quantum Hall Regime C. Sohrmann J. Oswald R.A. Romer 163

1 Introduction 163

2 The Quantized Hall Effect and Classical Percolation 165

3 Network Models at the IQHE 168

4 Hartree-Fock Approach to the IQHE 184

5 Conclusions 189

References 190

Percolative Quantum Transport in Manganites P. Majumdar 195

1 Introduction 195

2 Standard Quantum Percolation 196

3 Manganites: Phenomenology and Model 198

4 Percolative Effects in a One Band Model of Phase Competition 205

5 Percolation in Two Band Models with Electron-Phonon Coupling 217

6 Connection with Quantum Percolation and Resistor Networks 221

7 Conclusions 225

References 225

Classical and Quantum Breakdown in Disordered Materials D. Samanta B.K. Chakrabarti P. Ray 227

1 Introduction 227

2 Analysis of the Fuse Problem 229

3 Dielectric Breakdown Problem 238

4 Zener Breakdown in Anderson Insulators 247

5 Conclusions 249

References 249

Nonequilibrium Quantum Breakdown in a Strongly Correlated Electron System T. Oka H. Aoki 251

1 Introduction 251

2 Nonadiabatic Evolution and Pair Creation of Carriers 256

References 283

Percolation in Quantum Computation and Communication K. Kieling J. Eisert 287

1 Introduction 287

2 Percolation and Quantum Computing 290

3 Quantum Repeater Networks for Quantum Communication 307

4 Summary and Open Problems 315

References 317

Index 321