1. Diffusion Processes .......................................... 1
1.1. Introduction ............................................... 1
1.2. Brownian Motion and the Langevin Equation .................. 3
1.3. Langevin Equation from a System-plus-Bath Approach ......... 6
1.3.1. Ohmic Dissipation Model ............................. 9
1.4. Fokker-Planck and Master Equations ........................ 10
1.5. Two-State Jump Process .................................... 12
1.6. Single-Spin Kinetics from a System-plus-Bath Approach ..... 15
1.7. The Subsystem Density Operator ............................ 16
l.A. Appendix: Quantum Master Equation
Through a System-plus-Bath Approach ....................... 22
2. Kinetic Ising Models ........................................ 31
2.1. Introduction .............................................. 31
2.2. Equilibrium Properties in the Mean-Field Approximation .... 34
2.3. The Spin-Flip Glauber Model ............................... 37
2.3.1. Exact Dynamical Equations .......................... 37
2.3.2. Mean-Field Approximation ........................... 39
2.4. The Spin-Exchange Kawasaki Model .......................... 42
2.4.1. Exact Dynamical Equations .......................... 42
2.4.2. Mean-Field Approximation ........................... 44
2.5. Relaxation Kinetics in Homogeneous Systems ................ 45
2.6. Modeling of Order-Parameter Kinetics ...................... 48
2.6.1. Coarse-Grained Models from General
Considerations ..................................... 48
2.6.2. Coarse-Grained Models from Kinetic Ising Models .... 53
3. An Overview of Phase Ordering Dynamics ...................... 57
3.1. Introduction .............................................. 57
3.2. The Case with Nonconserved Order Parameter ................ 57
3.2.1. Scalar Order Parameter ............................. 57
3.2.2. Vector Order Parameter ............................. 62
3.3. The Case with Conserved Order Parameter ................... 64
3.3.1. Phase Separation without Hydrodynamic Effects ...... 65
3.3.2. Phase Separation with Hydrodynamic Effects ......... 68
3.4. Incorporation of Experimentally Relevant Effects .......... 71
4. Domain Growth in Systems with Quenched Disorder ............. 73
4.1. Introduction .............................................. 73
4.2. Phase Ordering Systems with Quenched Disorder ............. 74
4.2.1. Classification Scheme for Domain Growth Laws ....... 74
4.2.2. Random-Exchange Ising Model (REIM) ................. 76
4.2.3. Random-Field Ising Model (RFIM) .................... 80
4.3. Experimental Studies of Domain Growth with Disorder ....... 82
4.3.1. Domain Growth in the REIM .......................... 83
4.3.2. Domain Growth in the RFIM .......................... 84
4.4. Numerical Studies of Domain Growth with Disorder .......... 87
4.4.1. Monte Carlo Simulations ............................ 88
4.4.2. Simulations of Coarse-Grained Models ............... 89
4.4.3. Domain Growth in the REIM .......................... 92
4.4.4. Domain Growth in the RFIM ......................... 102
5. Surface-Directed Spinodal Decomposition
and Surface Enrichment ..................................... 105
5.1. Introduction ............................................. 105
5.2. Overview of Experimental Results ......................... 106
5.3. Theoretical Modeling ..................................... 1ll
5.3.1. Early Studies
of Surface-Directed Spinodal Decomposition ........ 1ll
5.3.2. Model Hamiltonian and Static Formalism ............ 113
5.3.3. Coarse-Grained Dynamical Model .................... 118
5.3.4. Static Solutions for a Short-Ranged Surface
Potential ......................................... 121
5.3.5. Characterization
of Surface-Directed Spinodal Decomposition ........ 122
5.4. Analytical and Numerical Results ......................... 123
5.4.1. Analytical Approaches to Early-time (Linear)
Behavior .......................................... 123
5.4.2. Wetting for Critical Quenches (ψ0 = 0) ............ 124
5.4.3. Wetting by the Minority Component (ψ0 < 0) ........ 127
5.4.4. Wetting by the Majority Component (ψ0 > 0) ........ 133
5.4.5. Other Relevant Studies for Case of Diffusive
Transport ......................................... 135
5.4.6. Role of Hydrodynamic Effects ...................... 136
5.5. Kinetics of Surface Enrichment for Stable Binary
Mixtures ................................................. 140
5.6. Asymptotic Properties of Enrichment Profiles ............. 144
6. Phase Ordering Dynamics in the Complex
Ginzburg-Landau Equation ................................... 147
6.1. Introduction ............................................. 147
6.2. Overview of Relevant Analytical Results .................. 148
6.3. Correlation Function for a Single-Spiral Morphology ...... 150
6.3.1. Case with β = 0 ................................... 154
6.3.2. Case with β ≠ 0 ................................... 156
6.4. Numerical Results for α = 2 .............................. 159
6.4.1. Spiral Growth Laws ................................ 160
6.4.2. Equal-Time Correlation Functions .................. 162
6.4.3. Equal-Time Structure Factors ...................... 165
6.5. Numerical Results for α = 3 .............................. 166
6.5.1. Spiral Growth Laws ................................ 168
6.5.2. Equal-Time Correlation Functions .................. 168
6.5.3. Equal-Time Structure Factors ...................... 169
6.6. Summary and Discussion ................................... 169
7. Quantum Dissipative Systems ................................ 173
7.1. Introduction ............................................. 173
7.2. Transverse Ising Model and Applications .................. 176
7.3. Static Behavior of the Transverse Ising Model
in Mean-Field Theory ..................................... 179
7.4. Relaxation Kinetics in Mean-Field Theory ................. 182
7.5. Quantum Glasses and Disordered Transverse Ising Model .... 185
7.6. Relaxation Kinetics in Magnetic Glasses .................. 190
7.7. Dielectric Relaxation in Proton Glasses .................. 195
7.A. Appendix: Matrix Elements of Ls and ∑(s = 0) ............. 199
8. Dissipative Two-State Systems .............................. 205
8.1. Spin-Boson Model ......................................... 205
8.1.1. Spin-Lattice Relaxation in Solids ................. 205
8.1.2. Dissipative Tunneling in a Symmetric Double
Well .............................................. 206
8.2. Dilute Bounce Gas Approximation (DBGA) ................... 208
8.3. Beyond the DBGA .......................................... 211
8.4. Dissipative Tunneling in an Asymmetric Double Well ....... 213
8.5. Asymmetric Double Well: The Weak-Coupling Limit .......... 218
8.6. Dynamics of an Impurity Spin
Coupled to a Spin-Boson System ........................... 222
8.7. Quantum Diffusion of Muons in Metals ..................... 227
8.8. Neutron Scattering Study of H-Tunneling in Niobium ....... 230
8.9. Spectroscopic Data in Kondo Systems ...................... 238
8.10.Two-level Systems in Glasses ............................. 243
9. Quantum Diffusion .......................................... 247
9.1. Introduction ............................................. 247
9.2. Quantum Diffusion of a Free Particle ..................... 249
9.3. Dynamics of a Charged Particle in a Magnetic Field ....... 251
9.4. Landau Diamagnetism in a Dissipative System .............. 255
10.Coherence and Decoherence .................................. 263
10.1.Introduction ............................................. 263
10.2.Landau Diamagnetism in a Dissipative System
Revisited ................................................ 267
10.3.Zeno Blocking of c-axis Transport in YBCO ................ 270
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