دانلود کتاب Bohmian Mechanics, Open Quantum Systems and Continuous Measurements

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Preface......Page 6
Contents......Page 13
1.1 Introduction......Page 16
1.2.1 Quantum Hydrodynamics Framework......Page 23
1.2.2 The Equations of Motion for One Particle......Page 27
1.2.3 Restricted Probability and Tubes......Page 38
1.2.4 Local and Expectation Values......Page 44
1.2.5 Complex Quantum Trajectories......Page 46
1.2.6 Many Particle Systems......Page 50
1.3.1 The Causal Stochastic Approach......Page 53
1.3.2 Diffusion. Quantum Brownian Motion......Page 55
1.3.3 Stochastic Weak Values......Page 61
1.3.4 The Density Matrix......Page 62
1.4 Dynamical Aspects of the Measuring Process......Page 65
References......Page 69
2.1 Introduction......Page 78
2.2 Ermakov--Bohm Invariants for the Time-Dependent Harmonic Oscillator......Page 79
2.3 Boundary Conditions in Tunneling......Page 86
2.4 Quantum Potential and Uncertainty Principle in Tunneling......Page 90
2.5 Scattering via Invariants of Bohmian Mechanics......Page 92
2.5.1 Quantum Traversal Time......Page 96
2.6 Wave Propagator for the Guiding Wave Function......Page 98
2.7 Bohmian Trajectories of Airy Packets......Page 101
2.8 Airy and Gaussian Slits. Quantum Focal Point......Page 106
2.9 Detection of Inertial and Gravitational Masses with Airy Wave Packets......Page 108
2.10 The Geometric Phase......Page 114
2.10.1 The Aharonov--Bohm Effect......Page 115
2.10.2 Quantum Vortices......Page 117
2.11 Bohmian Formulation of the Gross--Pitaevskii Equation......Page 118
2.12 Dissipation in the Caldirola-Kanai Model......Page 119
2.12.1 Free Gaussian Wave Packet......Page 123
2.12.2 Interference of Two Gaussian Wave Packets......Page 127
2.12.3 Linear Potential......Page 128
2.12.4 Damped Harmonic Oscillator......Page 130
References......Page 135
3.1 Introduction......Page 140
3.2 The Schrödinger--Langevin Equation......Page 144
3.3 The Schrödinger--Langevin--Bohm Equation......Page 149
3.4 The Ramsauer--Townsend Effect in a Dissipative Medium......Page 154
3.5 Tunneling Through a Dissipative Barrier......Page 162
3.6 The Plasma Fluid Formulation Within Bohmian Mechanics......Page 166
3.7 The Schrödinger Equation for an Extended Electron via Bohmian Mechanics......Page 168
3.8 Surface Diffusion......Page 171
3.8.1 The Bohmian--Brownian Motion......Page 179
3.8.2 The Harmonic Oscillator Motion......Page 184
3.9 The Generalized Schrödinger--Langevin--Bohm Equation......Page 186
References......Page 191
4 Continuous Quantum Measurements in the Bohmian Framework......Page 196
4.1 Introduction......Page 197
4.2 Measurement and the Characteristic Function......Page 198
4.3 A Short Introduction to Restricted Path Integrals......Page 206
4.3.1 Quantum Corridors......Page 211
4.3.2 Some Simple Applications of the RPI Formalism......Page 213
4.4.1 The Schrödinger Equation......Page 216
4.4.2 The Master Equation......Page 219
4.4.3 The Stochastic Schrödinger Equation......Page 220
4.5 The Nonlinear Schrödinger Equation for Continuous Measurement......Page 221
4.6 The Schrödinger--Langevin--Bohm Equation for Continuous Quantum Measurement......Page 223
4.7 Bohmian Time: Dividing Line Between Quantum and Classical Trajectories......Page 228
4.8 Some Simple Applications......Page 231
4.8.1 Stability of Quantum Stochastic Trajectories......Page 234
4.8.2 Free Gaussian Wave Packet......Page 237
4.8.3 Linear Potential......Page 240
4.8.4 Quadratic Potential......Page 241
4.8.5 The Schuch--Chung--Hartmann Equation for Continuous Quantum Measurement......Page 243
4.9 Classical and Quantum Lyapunov Exponents......Page 244
References......Page 248
Epilogue......Page 251
Index......Page 253