Time in Quantum Mechanics - Vol. 2 / Edition 1

by Gonzalo Muga, Andreas Ruschhaupt, Adolfo del Campo

Overview

But all the clocks in the city Began to whirr and chime: ’O let not Time deceive you, You cannot conquer Time. W. H. Auden It is hard to think of a subject as rich, complex, and important as time. From the practical point of view it governs and organizes our lives (most of us are after all attached to a wrist watch) or it helps us to wonderfully find our way in unknown territory with the global positioning system (GPS). More generally it constitutes the heartbeat of modern technology. Time is the most precisely measured quantity, so the second defines the meter or the volt and yet, nobody knows for sure what it is, puzzling philosophers, artists, priests, and scientists for centuries as one of the enduring enigmas of all cultures. Indeed time is full of contrasts: taken for granted in daily life, it requires sophisticated experimental and theoretical treatments to be accurately “produced. ” We are trapped in its web, and it actually kills us all, but it also constitutes the stuff we need to progress and realize our objectives. There is nothing more boring and monotonous than the tick-k of a clock, but how many fascinating challenges have physicists met to realize that monotony: Quite a number of Nobel Prize winners have been directly motivated by them or have contributed 1 significantly to time measurement.

Product Details

ISBN-13:	9783642031731
Publisher:	Springer Berlin Heidelberg
Publication date:	12/17/2009
Series:	Lecture Notes in Physics , #789
Edition description:	2010
Pages:	423
Product dimensions:	6.10(w) x 9.20(h) x 1.20(d)

Table of Contents

1 Memories of Old Times: Schlick and Reichenbach on Time in Quantum Mechanics José M. Sánchez-Ron 1

1.1 Introduction: The New Physics, via Relativity, Attracts the Philosophers 1

1.2 Time in Quantum Physics: The Time-Energy Uncertainty Relation 3

1.3 Schlick on Quantum Theory 7

1.4 Reichenbach on Time in Quantum Physics 8

1.5 Reichenbach on Feynman's Theory of the Positron 10

1.6 Epilogue 11

References 12

2 The Time-Dependent Schrodinger Equation Revisited: Quantum Optical and Classical Maxwell Routes to Schrödinger's Wave Equation Marlan O. Scully 15

2.1 Introduction 15

2.2 The Quantum Optical Route to the Time-Dependent Schrödinger Equation 16

2.3 The Classical Maxwell Route to the Schrödinger Equation 19

2.4 The Single Photon and Two Photon Wave Functions 21

2.5 Conclusions 22

References 23

3 Post-Pauli's Theorem Emerging Perspective on Time in Quantum Mechanics Eric A. Galapon 25

3.1 Introduction 25

3.2 Quantum Canonical Pairs 27

3.3 Time of Arrival Operators 33

3.4 Confined Time of Arrival Operators 44

3.5 Conjugacy of the Confined Time of Arrival Operators 46

3.6 Dynamics of the Eigenfunction of the Confined Time of Arrival Operators 52

3.7 Dynamical Behaviors in the Limit of Large Confining Lengths and the Appearance of Particle 55

3.8 Quantum Time of Arrival Distribution 58

3.9 Conclusion 61

References 62

4 Detector Models for the Quantum Time of Arrival Andreas Ruschhaupt J. Gonzalo Muga Gerhard C. Hegerfeldt 65

4.1 The Time of Arrival in Quantum Mechanics 65

4.2 The Basic Atom-Laser Model 70

4.3 Complex Potentials 76

4.4 Quantum Arrival Times and Operator Normalization 82

4.5 Kinetic Energy Densities 87

4.6 Disclosing Hidden Information Behind the Quantum Zeno Effect: Pulsed Measurement of the Quantum Time of Arrival 89

4.7 Summary 93

References 94

5 Dwell-Time Distributions in Quantum Mechanics José Muñoz Iñigo L. Egusquiza Adolfo del Campo Dirk Seidel J. Gonzalo Muga 97

5.1 Introduction 97

5.2 The Dwell-Time Operator 99

5.3 The Free Particle Case 102

5.4 The Scattering Case 106

5.5 Some Extensions 111

5.6 Relation to Flux-Flux Correlation Functions 115

5.7 Final Comments 123

References 124

6 The Quantum Jump Approach and Some of Its Applications Gerhard C. Hegerfeldt 127

6.1 Introduction 127

6.2 Repeated Measurements on a Single System: Conditional Time Development, Reset Operation, and Quantum Trajectories 129

6.3 Application: Macroscopic Light and Dark Periods 141

6.4 The General N-Level System and Optical Bloch Equations 145

6.5 Quantum Counting Processes 150

6.6 How to Replace Density Matrices by Pure States in Simulations 154

6.7 Inclusion of Center-of-Mass Motion and Recoil 161

6.8 Extension to Spin-Boson Models 165

6.9 Discussion 170

References 173

7 Causality in Superluminal Pulse Propagation Robert W. Boyd Daniel J. Gauthier Paul Narum 175

7.1 Introduction 175

7.2 Descriptions of the Velocity of Light Pulses 176

7.3 History of Research on Slow and Fast Light 178

7.4 The Concept of Simultaneity 185

7.5 Causality and Superluminal Pulse Propagation 187

7.6 Quantum Mechanical Aspects of Causality and Fast Light 191

7.7 Numerical Studies of Propagation Through Fast-Light Media 194

7.8 Summary 202

References 202

8 Experiments on Quantum Transport of Ultra-Cold Atoms in Optical Potentials Martin C. Fischer Mark G. Raizen 205

8.1 Introduction 205

8.2 Experimental Apparatus 211

8.3 Details of the Interaction 212

8.4 Quantum Transport 213

8.5 Quantum Tunneling 225

8.6 Conclusions 236

References 236

9 Quantum Post-exponential Decay Joan Martorell J. Gonzalo Muga Donald W.L. Sprung 239

9.1 Introduction 239

9.2 Simple Models and Examples 247

9.3 Three-Dimensional Models of a Particle Escaping from a Confining Potential 252

9.4 Physical Interpretation of Post-exponential Decay 258

9.5 Toward Experimental Observation 261

9.6 Final Comments 271

References 272

10 Timescales in Quantum Open Systems: Dynamics of Time Correlation Functions and Stochastic Quantum Trajectory Methods in Non-Markovian Systems Daniel Alonso Inés de Vega 277

10.1 Introduction 277

10.2 Atoms in a Structured Environment, an Example of Non-Markovian Interaction 278

10.3 Two Complementary Descriptions of the Dynamics of a Quantum Open System 279

10.4 Dynamics of Multiple Time Correlation Functions 284

10.5 Examples 291

10.6 Discussion and Conclusions 298

References 299

11 Double-Slit Experiments in the Time Domain Gerhard G. Paulus Dieter Bauer 303

11.1 Introduction 303

11.2 Wave Packet Interference in Position and Momentum Space 304

11.3 Time-Domain Double-Slit Experiments 313

11.4 Strong-Field Approximation and Interfering Quantum Trajectories 325

References 337

12 Optimal Time Evolution for Hermitian and Non-Hermitian Hamiltonians Carl M. Bender Dorje C. Brody 341

12.1 Introduction 341

12.2 PT Quantum Mechanics 342

12.3 Complex Classical Motion 346

12.4 Hermitian Quantum Brachistochrone 347

12.5 Non-Hermitian Quantum Brachistochrone 354

12.6 Extension of Non-Hermitian Hamiltonians to Higher-Dimensional Hermitian Hamiltonians 358

References 360

13 Atomic Clocks Robert Wynands 363

13.1 Introduction 363

13.2 Why We Need Clocks at All 364

13.3 What Is a Clock? 368

13.4 How an Atomic Clock Works 369

13.5 The "Classic" Caesium Clock 372

13.6 The Ramsey Technique 375

13.7 Atomic Fountain Clocks 379

13.8 Other Types of Atomic Clocks 396

13.9 Optical Clocks 402

13.10 The Future (Maybe) 407

13.11 Precision Tests of Fundamental Theories 409

13.12 Conclusion 412

References 412

Index 419