A Guide to Monte Carlo Simulations in Statistical Physics, Second Edition

1562titl......Page 1
1562pref......Page 5
1562toc......Page 7
1562cont......Page 10
1562abbr......Page 15
1 Introduction......Page 16
2 Testable Models for Experiments......Page 19
3 Lunar Laser Ranging......Page 23
5 Interplanetary Laser Ranging......Page 24
6 A STEP Experiment......Page 26
References......Page 27
1 Introduction......Page 28
2 Currently Running Experiments......Page 29
3 The Principle of Our Experiment......Page 32
4 The Experimental Setup......Page 34
5 The Measuring Procedure and First Results......Page 37
6 Outlook......Page 38
Acknowledgment......Page 39
References......Page 40
1 Introduction......Page 42
2 Rotation......Page 43
3 Equation of Motion for Angular Momentum......Page 44
3.1 The Motion of Gyroscopes......Page 45
3.2 Motion of an Elementary Particle with Spin 1/2......Page 48
4.1 Stationary Gravitational Field......Page 51
4.2 Gravitational Field of a RotatingSource......Page 52
5.2 Motion of a Gyroscope......Page 54
6 On the Observation of Gravitomagnetic Effects......Page 56
6.2 Lense –Thirring Effect for Gyroscopes......Page 57
6.3 Lense –Thirring Effect in Quantum Physics......Page 59
Appendix: Theory of Congruences......Page 60
References......Page 61
1 Gravity Probe B: An Experiment in Physics – and Management......Page 63
2 Shape of the Experiment......Page 65
3 Incremental Prototyping......Page 69
4 Risk Mitigation and Verification Matrix......Page 71
5 Probe-C Assembly March –August 1999......Page 77
6 Probe-C Testing in Science Mission Dewar August –December 1999......Page 80
7 The Four Discrepancies and Their Resolution August 1999 –June 2000......Page 82
8.1 Spacecraft......Page 89
8.2 Payload Electronics......Page 91
8.3 Integration &Test,Ground Station,and Launch......Page 92
Acknowledgement......Page 93
1 Introduction......Page 94
2 Gravitoelectromagnetism......Page 95
2.2 Gravitoelectromagnetic Field......Page 96
2.3 Free Fall Is Not Universal......Page 100
2.4 GEM Stress-Energy Tensor......Page 101
2.5 Oscillations of a Charged Rotating Black Hole......Page 104
3 Structure of Time and Relativistic Precession......Page 105
4 Clock Effect in the PPN Approximation......Page 108
5 Detection of the Gravitomagnetic Temporal Structure......Page 111
6 Quantum Origin of Inertia......Page 112
7 Discussion......Page 115
Appendix: Mach and the Absolute Motion of Light......Page 116
References......Page 117
1 Introduction......Page 120
2.1 The Problem with the Covariant Equations of Motion......Page 121
2.2 What Is the Correct Definition of the Coordinate of a Spinning Particle?......Page 123
2.3 The Noncovariant Formalism......Page 124
3.1 General Relationships......Page 125
3.2 Spin –Orbit Interaction......Page 127
3.3 Spin –Orbit Interaction in the Schwarzschild Field......Page 128
3.5 Spin Precession in a Plane Gravitational Wave......Page 129
4.2 Second-Order Spin Effects in an Electromagnetic Field......Page 130
4.3 Second-Order Spin Effects in a Gravitational Field......Page 132
5 Multipoles of Black Holes......Page 134
6.1 Spin Interactions in a Two –Body Problem......Page 135
6.2 Contribution of Spin Interactions to Gravitational Radiation......Page 137
References......Page 138
2 The GEO 600 Concept......Page 140
3 Noise Contributions......Page 141
3.2 Thermal Noise......Page 142
3.3 Laser Noise......Page 143
6 Interferometry......Page 144
8.1 Vacuum Pumps......Page 146
9 The 30 Meter Prototype......Page 147
References......Page 149
1 Introduction......Page 150
2.1 Einstein Field Equations......Page 153
2.2 Multipole Expansion in Linearized Gravity......Page 155
3.1 Multipole Expansion in the Far Region......Page 157
3.2 The Far-Field Quadrupole Formula......Page 158
3.3 Energy Balance Equation and Radiation Reaction......Page 160
4.1 The Multipole Moments in the Post-Newtonian Approximation......Page 162
4.2 Post-Newtonian Radiation Reaction......Page 166
5.1 General Solution of the Light Propagation Equation......Page 168
5.2 Time Delay and Bendingof Light......Page 170
6 Detection of Gravitational Waves......Page 172
References......Page 173
1 Introduction......Page 176
2 Cosmological Gravitational Waves......Page 179
3 Cosmological Pump Field......Page 183
4 Solving Gravitational Wave Equations......Page 186
5 Theoretical and Observational Constraints......Page 191
6 Detectability of Relic Gravitational Waves......Page 195
7 Conclusion......Page 199
References......Page 200
1.1 From the Weak to Einstein ’s Equivalence Principle......Page 202
1.2 Theoretical Contexts for Analyses of the EEP......Page 204
1.3 The Role of Locality......Page 205
1.4 Relevant Observables......Page 206
2 Theoretical Frameworks for the Analysis of EEP Tests......Page 208
2.1 The TH µ–Formalism......Page 209
2.4 Formalisms Based on Matter –Field Equations of Motion......Page 210
3.1 StringTheory......Page 212
3.2 Loop Quantum Gravity......Page 213
4.1 Tests of the Universality of Freefall......Page 214
4.2 Spectroscopic and Atomic Clock Tests of the EEP......Page 215
4.3 EEP Tests Involving Observations of Wave Propagation......Page 216
References......Page 217
1 Background......Page 220
2 STEP Concepts......Page 222
3 STEP Instrument Configuration......Page 224
3.1 Test Mass Shapes and Con .guration......Page 229
3.2 Differential Accelerometer Operation......Page 230
4 Experiment Operations and Timeline......Page 232
4.1 Test for Systematic Effects......Page 235
5 Error Analysis and Mission Tradeoffs......Page 240
5.2 Satellite Rotation and EP Signal Detection in the Error Model......Page 241
References......Page 253
1 Introduction......Page 255
2.1 Drop Tower Bremen......Page 256
2.2 Experimental Set –Up and Timing......Page 258
2.3 Main Error Sources......Page 259
3 SQUID Based Position Detector......Page 262
3.1 The DC SQUID......Page 263
3.2 SQUID Control Unit......Page 264
3.3 Detector Principle......Page 266
4.2 Performance of the Detector......Page 272
4.3 Free Fall Measurement System......Page 273
4.4 Free Fall Tests of the Measurement System......Page 274
Acknowledgement......Page 278
References......Page 279
1 Introduction......Page 280
2 Accelerometers Dedicated to Space......Page 283
3 Electrostatic Servo –Controlled Accelerometer Operation......Page 284
4 The ASTRE and STAR Accelerometers......Page 286
5 From CHAMP to GRACE and GOCE Instrument......Page 292
6 Electrostatic Accelerometers to Test the Equivalence Principle in Space......Page 293
7 Space Gravity Wave Antenna......Page 294
8 Perspective......Page 296
References......Page 297
1 Introduction......Page 299
2.1 Overview......Page 300
2.2 Yukawa Potentials......Page 301
2.3 Current Constraints on New Yukawa Forces......Page 303
3.1 General Problems......Page 304
3.2 Quantitative Example:Parallel Plate Gravity Experiment......Page 305
4.1 Null Experiment #1......Page 310
4.2 Null Experiment #2......Page 313
5 Discussion......Page 314
References......Page 315
1 Introduction......Page 317
2 Restricted Three-Body Problem in General Relativity......Page 318
References......Page 322
1 Introduction......Page 324
2 Dynamical Equations for Bodies,Light,and Clocks......Page 326
3 New Long Range Force?......Page 329
4 LLR ’s Science –Related Range Signals......Page 330
5 The Gravitomagnetic Interaction......Page 334
6 Inductive (Inertial)Forces......Page 335
References......Page 336
1 Introduction......Page 337
2 ASTROD Payload Concept and Technological Development Requirements......Page 339
3 Orbit Simulation......Page 340
3.2 Simulation of ASTROD Ranging Data......Page 342
3.3 Estimation of Parameters......Page 343
4 Solar Angular Momentum and Solar Oscillations......Page 344
5 G –Wave Detection......Page 346
7 Outlook......Page 348
References......Page 349
1 Introduction......Page 351
2.1 Definitions......Page 352
2.2 Perturbing Effects and Remedies......Page 353
3.1 Cs Beam Machine......Page 355
3.3 Atomic Fountain Clocks......Page 356
3.4 Clocks Based on Ion Traps......Page 359
4.1 Clocks Based on Ion Traps......Page 361
4.3 ExpandingCloud of Cold Ballistic Ca Atoms......Page 362
5 Measurement of Optical Frequencies......Page 364
6 Optical Frequency Standards for the Realization of the Meter......Page 366
References......Page 367
1 Introduction......Page 373
2 Motivation......Page 375
3 The Tri –clock Instrument......Page 376
4.1 Spacecraft......Page 381
5 Conclusions......Page 383
References......Page 384
1 The Pulsar Population......Page 385
2 Pulsar Timing......Page 387
3.1 PSR B1913+16......Page 392
3.2 PSR B1534+12......Page 393
4 Binary Pulsars and Gravity Experiment II. Small –Eccentricity Binary Pulsars......Page 395
4.1 Gravitational Dipole Radiation......Page 396
4.2 Violation of the Strong Equivalence Principle......Page 397
4.3 Violation of Local Lorentz Invariance and Conservation Laws......Page 398
5 Geodetic Precession......Page 399
References......Page 401
1 Introduction......Page 404
2 Lagrangian Theory......Page 405
3.1 Dificulties with the Derivative Coupling......Page 407
3.2 A Coherent Method f Quantization......Page 410
4 Interaction Picture and the S –Matrix......Page 412
4.1 Evolution Operator and Transition Amplitudes......Page 413
4.2 S –Matrix......Page 416
5 Calculation of the Relativistic Phase Shifts in the Weak –Field Approximation......Page 417
5.1 Calculation in Configuration Space......Page 418
5.2 Calculation in the Momentum Representation......Page 419
5.3 Analogy with the Electromagnetic Interaction......Page 429
Appendix A: Dirac Equation in Curved Space –Time......Page 430
Appendix B: Weak-Field Approximation......Page 431
Appendix C: A Stationary Phase Calculation......Page 434
Appendix D: Derivation of the Wave Function Using the Momentum Representation......Page 435
References......Page 437
1 Introduction......Page 440
2 WEP,EEP and the Axial Interaction......Page 441
3 Spin and Gravitation......Page 443
4 Spin, Equivalence Principle,and Long –Range Forces......Page 444
5 Experimental Searches for Photon Polarization Coupling and Tests of EEP......Page 445
6 Experimental Searches for Electron Spin –Coupling......Page 447
6.1 Weak Equivalence Principle Experiments......Page 448
6.2 Finite –Range Spin –Coupling Experiments......Page 449
6.3 Spin –Spin CouplingExperiments......Page 451
6.4 Cosmic Spin –Coupling Experiments......Page 452
7 Outlook......Page 453
References......Page 454
1 The Dirac Equation......Page 458
2 Spin and the Poincaré Group......Page 460
References......Page 463
1 Introduction......Page 464
2 The Model: A Modification of the Dirac Equation......Page 466
3 Plane Wave Solutions and Neutrino Propagation......Page 467
4.1 The Non –relativistic Field Equation......Page 470
4.2 Modifications of the Energy Levels......Page 472
5 Conclusion......Page 475
References......Page 476
1 Introduction......Page 478
2 On the Equivalence Principle......Page 480
3 A Caveat......Page 481
4 Electric Charge and Magnetic Flux Conservation......Page 483
5 No Interaction of Charge and Flux “Substrata” with Gravity......Page 485
6.1 Non-local......Page 486
6.2 Non-linear......Page 488
6.3 Linear: Abelian Axion, inter Alia......Page 490
6.4 Isotropic......Page 492
6.5 Centrosymmetric......Page 495
7.1 Non-minimal Coupling Violating Charge and/or Flux Conservation......Page 496
7.2 “Admissible” Non-minimal Coupling......Page 497
8 Outlook......Page 498
References......Page 499
1562indx......Page 504