Biblioteka Instytutów Fizyki

1 The InAs/GaAs(001) Quantum Dots Transition: Advances on Understanding . . 1
2 Self-assembly of InAs Quantum Dot Structures on Cleaved Facets . . 25
3 InAs/GaAs Quantum Dots with Multimodal Size Distribution . . 43
4 Carrier Transfer in the Arrays of Coupled Quantum Dots . . 67
5 Dynamics of Carrier Transfer into In(Ga)As Self-assembled Quantum Dots . . 129
6 Spin Phenomena in Self-assembled Quantum Dots . . 165
7 Excitons and Spins in Quantum Dots Coupled to a Continuum of States . . 217
8 Quantum Coupling in Quantum Dot Molecules . . 239
9 Studies of Semiconductor Quantum Dots for Quantum Information Processing . . 267
10 Stress Relaxation Phenomena in Buried Quantum Dots . . 297
11 Capacitance-Voltage Spectroscopy of In As Quantum Dots . . 337
12 In(Ga)As/GaAs Quantum Dots Grown by MOCVD for Opto-electronic Device Applications . . 359
13 Area-selective and Site-controlled InAs Quantum-dot
14 Detailed Analysis of the Shape-dependent Deformation Field in 3D Ge Islands on Si(001) . . 421
15 Growth and Characterization of Ill-Nitride Quantum Dots and their Application to Emitters . . 439
Subject Index . . 461

Preface

Part 1 Introduction to Materials Physics
1.1 Crystallography . . 2
1.2 Quantum mechanics . . 10
1.3 Solid state physics . . 34
1.4 X-ray diffraction . . 50
1.5 Thermal properties of solids . . 73
1.6 Mechanical properties of solids . . 83

Part 2 Dielectric Properties of Materials
2.1 Dielectric properties . . 91
2.2 Polanzability . . 107
2.3 Ferroelectric and piezoelectric materials . . 116
2.4 Dielectric breakdown . . 127
2.5 Examples of dielectrics . . 132

Part 3 Magnetic Properties of Materials
3.1 Magnetic field . . 141
3.2 Magnetic moment . . 148
3.3 Magnetic properties . . 157
3.4 Ferromagnetism . . 188
3.5 Superconductivity . . 188

Index . . 193

Introduction to Grid Infrastructures . . 1
How to Port Applications on Grid: A Short Review . . 15
GRIDSEED: A Virtual Training Grid Infrastructure . . 39
Porting Applications to the Grid . . 55
On the Structuring of a Molecular Simulator as a Grid Service . . 63
Ab Initio Electronic Structure Computations on EGEE Grid . . 83
Q5Cost Format and Library: A Tutorial About the Common Format for Quantum Chemistry Interoperability . . 103
Protein Folding by Bias Exchange Metadynamics on a Grid Infrastructure . . 125
On the Grid Implementation of a Quantum Reactive Scattering Program . . 145
Calculation of Phonon Dispersions on the Grid Using Quantum ESPRESSO . . 163
Exploiting Grids for Applications in Condensed Matter Physics . . 187
Implementation of a Semiclassical Initial Value Representation Code
on the Grid to Calculate Rate Coefficients of Atom Diatom Reaction . . 203

Preface . . vii
Chapter 1: The Method of Characteristics for the Numerical Solution of Hyperbolic Differential Equations . . 1
Chapter 2: Modeling and Simulation of Semiconductor Optical Amplifier Dynamics for Telecommunication Applications . . 89
Chapter 3: Computer Simulation of Radon Measurements with Nuclear Track Detectors . . 125
Chapter 4: Effects of Round-off Errors on Molecular Dynamics Simulations . . 157
Chapter 5: Bi-Dimensional Quantum Tunneling by a Time Dependent Computational Approach . . 185
Chapter 6: Dielectric Confinement in Quantum Dots . . 211
Chapter 7: Painleve Analysis and Symmetries: (2+l)-D Nonlinear Wave Equation Arising in a One-Dimensional Model for the 3D Vorticity Equation . . 233
Chapter 8: Computers and Liquid State Statistical Mechanics . . 243
Index . . 265

Preface . . xi
1. INTRODUCTION . . 1
2. GASDYNAMIC THEORY OF DETONATIONS AND DEFLAGRATIONS . . 26
3. DYNAMICS OF DETONATION PRODUCTS . . 53
4. LAMINAR STRUCTURE OF DETONATIONS . . 73
5. UNSTABLE DETONATIONS: NUMERICAL DESCRIPTION . . 98
6. UNSTABLE DETONATIONS: EXPERIMENTAL OBSERVATIONS . . 147
7. INFLUENCE OF BOUNDARY CONDITIONS . . 204
8. DEFLAGRATION-TO-DETONATION TRANSITION . . 250
9. DIRECT INITIATION OF DETONATIONS . . 297
Epilogue . . 373
Index . . 377

1 Rotational Alignment and Bandcrossings . . 1
1.1 Introduction . . 1
1.2 Rotational Alignment and Bandcrossings . . 2
1.3 Systematics of Bandcrossings . . 7
1.4 Comments and Conclusions . . 20
References . . 21

2 Magnetic Rotation . . 23
2.1 Introduction . . 23
2.2 Magnetic Rotational Bands in the Pb Region . . 25
2.3 Antimagnetic Rotation . . 50
References . . 53

3 Triaxial Strong Deformation and Wobbling Motion . . 55
3.1 Introduction . . 55
3.2 Triaxial Strong Deformation . . 55
3.3 Triaxiality and Wobbling Motion . . 59
3.4 Experimental Results—Even-N Lu Isotopes . . 61
3.5 Discussion . . 70
3.6 Conclusion, Status and Outlook . . 76
References . . 78

4 Chirality in Nuclei . . 81
4.1 Introduction . . 81
4.2 The Nuclear Chiral Phenomenon . . 81
4.3 Fingerprints of Nuclear Chirality . . 83
4.4 A Experimental Results . . 84
4.5 Discussion . . 99
4.6 Conclusions and Perspectives . . 109
References . . 110

Partial List of Books, Review and Some Other Articles Mainly in High Spin Nuclear Structure Physics . . 113

Index . . 119

Preface . . xi
Conventions . . xiv

1 Aperitifs . . 1
1.1 Diffusion . . 1
1.2 Single-species annihilation/coalescence . . 4
1.3 Two-species annihilation . . 9
1.4 Notes . . 10

2 Diffusion . . 12
2.1 The probability distribution . . 12
2.2 Central limit theorem . . 15
2.3 Walks with broad distributions . . 17
2.4 Application to gravity: the Holtsmark distribution . . 22
2.5 First-passage properties . . 26
2.6 Exit probabilities and exit times . . 30
2.7 Reaction rate theory . . 37
2.8 The Langevin approach . . 40
2.9 Application to surface growth . . 44
2.10 Notes . . 51
2.11 Problems . . 51

3 Collisions . . 59
3.1 Kinetic theory . . 51
3.2 The Lorentz gas . . 63
3.3 Lorentz gas in an external field . . 70
3.4 Collisional impact . . 75
3.5 Maxwell molecules and very hard particles . . 77
3.6 Inelastic gases . . 81
3.7 Ballistic agglomeration . . 89
3.8 Single-lane traffic . . 92
3.9 Notes . . 96
3.10 Problems . . 97

4 Exclusion . . 103
4.1 Symmetric exclusion process . . 103
4.2 Asymmetric exclusion process . . 108
4.3 Hydrodynamic approach . . 112
4.4 Microscopic approach . . 118
4.5 Open systems . . 123
4.6 Notes . . 130
4.7 Problems . . 131

5 Aggregation . . 134
5.1 The master equations . . 134
5.2 Exact solution methods . . 137
5.3 Gelation . . 145
5.4 Scaling . . 153
5.5 Aggregation with input . . 156
5.6 Exchange-driven growth . . 163
5.7 Notes . . 167
5.8 Problems . . 168

6 Fragmentation . . 172
6.1 Binary fragmentation . . 172
6.2 Planar fragmentation . . 180
6.3 Reversible polymerization . . 185
6.4 Collisional fragmentation . . 191
6.5 Notes . . 195
6.6 Problems . . 195

7 Adsorption . . 199
7.1 Random sequential adsorption in one dimension . . 199
7.2 Phase space structure . . 206
7.3 Adsorption in higher dimensions . . 213
7.4 Reversible adsorption . . 220
7.5 Polymer translocation . . 226
7.6 Notes . . 229
7.7 Problems . . 230

8 Spin dynamics . . 233
8.1 Phenomenology of coarsening . . 233
8.2 The voter model . . 235
8.3 Ising-Glauber model . . 244
8.4 Mean-field approximation . . 247
8.5 Glauber dynamics in one dimension . . 249
8.6 Glauber dynamics in higher dimensions . . 258
8.7 Spin-excnange dynamics . . 264
8.8 Cluster dynamics . . 269
8.9 Notes . . 273
8.10 Problems . . 274

9 Coarsening . . 277
9.1 Models . . 277
9.2 Free evolution . . 280
9.3 Case studies in non-conservative dynamics . . 283
9.4 Final states . . 292
9.5 Defects . . 294
9.6 Conservative dynamics . . 302
9.7 Extremal dynamics . . 307
9.8 Nucleation and growth . . 312
9.9 Notes . . 317
9.10 Problems . . 318

10 Disorder . . 322
10.1 Disordered spin chain . . 322
10.2 Random walk in a random potential . . 331
10.3 Random walk in random velocity fields . . 339
10.4 Notes . . 343
10.5 Problems . . 343

11 Hysteresis . . 346
11.1 Homogeneous f erromagnets . . 346
11.2 Perturbation analysis . . 349
11.3 Disordered ferromagnets . . 357
11.4 Mean-field model . . 361
11.5 Hysteresis in the random-field Ising chain . . 366
11.6 Notes . . 370
11.7 Problems . . 370

12 Population dynamics . . 373
12.1 Continuum formulation . . 373
12.2 Discrete reactions . . 382
12.3 Small-fluctuatHi expansion . . 391
12.4 Large fluctuations . . 394
12.5 Notes . . 399
12.6 Problems . . 400

13 Diffusive reactions . . 404
13.1 Role of the spatial dimension . . 404
13.2 The trapping reaction . . 409
13.3 Two-species annihilation . . 414
13.4 Single-species reactions in one dimension . . 417
13.5 Reactions in spatial gradients . . 428
13.6 Notes . . 436
13.7 Problems . . 437

14 Complex networks . . 441
14.1 Non-lattice networks . . 441
14.2 Evolving random graphs . . 443
14.3 Random recursive trees . . 451
14.4 Preferential attachment . . 456
14.5 Fluctuations in networks . . 460
14.6 Notes . . 465
14.7 Problems . . 466

References . . 471
Index . . 483

FOREWORD . . vii
PROLOGUE . . 1
1 AN END AND A BEGINNING . . 7
2 TRAINING FOR COSMOLOGY . . 31
3 THE STAR MAKERS . . 60
4 HOYLE'S SECRET WAR . . 81
5 THE NATURE OF THE UNIVERSE . . 108
6 LIVES OF THE STARS . . 142
7 CLASH OF TITANS . . 167
8 ORIGIN OF THE CHEMICAL ELEMENTS . . 197
9 MATTERS OF GRAVITY . . 223
10 MOUNTAINS TO CLIMB . . 255
11 THE WATERSHED . . 277
12 STONES, BONES, BUGS AND ACCIDENTS . . 293

ACKNOWLEDGEMENTS . . 324
NOTES . . 326
BIBLIOGRAPHY . . 345
INDEX . . 354

Preface . . xi

1 General Theory of Integration
1.1 Measurable spaces, o-algebras . . 1
1.2 Measurable spaces and topological spaces . . 3
1.3 Structure of measurable functions . . 15
1.4 Positive measures . . 17
1.5 Integrating non-negative functions . . 22
1.6 Three basic convergence theorems . . 28
1.7 Space L1(u) and negligible sets . . 34
1.8 Notes . . 39
1.9 Exercises . . 41

2 Actual Construction of Measure Spaces
2.1 Partitions of unity . . 67
2.2 The Riesz Markov representation theorem . .70
2.3 Producing positive Radon measures . . 82
2.4 The Lebesgue measure on Rm, properties arid characterization . . 86
2.5 Caratheodory theorem on outer measures . . 93
2.6 Hausdorff measures, Hausdorff dimension . . 96
2.7 Notes . . 102
2.8 Exercises . . 103

3 Spaces of Integrable Functions
3.1 Convexity inequalities (Jensen, Holder, Minkowski) . . 125
3.2 Lp spaces . . 132
3.3 Integrals depending on a parameter . . 140
3.4 Continuous functions in Lp spaces . . 147
3.5 On various notions of convergence . . 152
3.6 Notes . . 154
3.7 Exercises . . 155

4 Integration on a Product Space
4.1 Product of measurable spaces . . 189
4.2 Tensor product of sigma-finite measures . . 192
4.3 The Lebosgue measure 011 Rm and tensor products . . 199
4.4 Notes . . 200
4.5 Exercises . . 201

5 Diffeomorphisms of Open Subsets of Rn and Integration
5.1 Differentiability . . 219
5.2 Linear transformations . . 223
5.3 Change-of-vanables formula . . 228
5.4 Examples, polar coordinates in Rn . . 233
5.5 Integration on a C1 hypersurface of the Euclidean Rn . . 238
5.6 More on Hausdorff measures on Rn . . 242
5.7 Cantor sets . . 249
5.8 Category arid measure . . 262
5.9 Notes . . 264
5.10 Exercises . . 266

6 Convolution
6.1 The Banach algebra L1(Rn) . . 283
6.2 Lp Estimates for convolution, Young's inequality . . 288
6.3 Weak Lp spaces . . 293
6.4 The Hardy Littlewood-Sobolev inequality . . 297
6.5 Notes . . 301
6.6 Exercises . . 302

7 Complex Measures
7.1 Complex measures . . 317
7.2 Total variation of a complex measure . . 319
7.3 Absolute continuity, mutually singular measures . . 321
7.4 Radon Nikodym theorem . . 323
7.5 The dual of LP(X, M,u), 1 < p < +00 . .  327
7.6 Notes . . 333
7.7 Exercises . . 334

8 Basic Harmonic Analysis on Rn
8.1 Fouier transform of tempered distributions . . 343
8.2 The Poisson summation formula . . 357
8.3 Periodic distributions . . 361
8.4 Notes . . 365
8.5 Exercises . . 366

9 Classical Inequalities
9.1 Riesz-Thorin interpolation theorem . . 371
9.2 Marcinkiewicz Interpolation Theorem . . 380
9.3 Maximal function . . 383
9.4 Lebesgue differentiation theorem, Lebesgue points . . 386
9.5 Gagliardo-Nirenberg inequality . . . . 389
9.6 Sobolev spaces, Sobolev injection theorems . . 394
9.7 Notes . . 399
9.8 Exorcises . . 400

10 Appendix
10.1 Set theory, cardinals, ordinals . . 407
10.2 Topological matters (Tychonoff, Hahn-Bariach, Baire) . . 425
10.3 Duality in Banach spaces (weak convergence, reflexivity) . . 440
10.4 Calculating antiderivatives (classics, Abelian, Gaussian) . . 448
10.5 Some special functions (logarithm, Gamma function, Laplacean) . . 461
10.6 Classical volumes and areas (balls, spheres, cones, polyhedra) . . 474

Bibliography . . 481
Index . . 487