Time in Quantum Mechanics

by Muga, Gonzalo; Ruschhaupt, Andreas; Del Campo, Adolfo

• ISBN13: 9783642031731
• ISBN10: 3642031730
• Format: Hardcover
• Copyright: 2010-02-03
• Publisher: Springer Verlag

Summary

The treatment of time in quantum mechanics continues to be an important and challenging open question in the foundation of the quantum theory. This book is the second volume (following LNP 734 Time in Quantum Mechanics ' Vol. 1) to introduce and to describe the problems, attempts and achievements in defining, formalizing and measuring different time quantities in quantum theory, as well as related issues. Written as an introductory guide for newcomers to the subject, it will also be a useful reference for the expert. After a brief historical overview in the first chapter, eleven tutorial reviews cover many open questions regarding fundamental concepts and time observables, as well as a number of quantum dynamical effects and their associated characteristic time scales. Last but not least, a tutorial review on atomic clocks explains that while we do not know what time is, we know very well how to measure it with an accuracy like no other physical parameter

Table of Contents

Memories of Old Times: Schlick and Reichenbach on Time in Quantum Mechanics	p. 1
Introduction: The New Physics, via Relativity, Attracts the Philosophers	p. 1
Time in Quantum Physics: The Time-Energy Uncertainty Relation	p. 3
Schlick on Quantum Theory	p. 7
Reichenbach on Time in Quantum Physics	p. 8
Reichenbach on Feynman's Theory of the Positron	p. 10
Epilogue	p. 11
References	p. 12
The Time-Dependent Schrodinger Equation Revisited: Quantum Optical and Classical Maxwell Routes to Schrödinger's Wave Equation	p. 15
Introduction	p. 15
The Quantum Optical Route to the Time-Dependent Schrödinger Equation	p. 16
The Classical Maxwell Route to the Schrödinger Equation	p. 19
The Single Photon and Two Photon Wave Functions	p. 21
Conclusions	p. 22
References	p. 23
Post-Pauli's Theorem Emerging Perspective on Time in Quantum Mechanics	p. 25
Introduction	p. 25
Quantum Canonical Pairs	p. 27
Time of Arrival Operators	p. 33
Confined Time of Arrival Operators	p. 44
Conjugacy of the Confined Time of Arrival Operators	p. 46
Dynamics of the Eigenfunction of the Confined Time of Arrival Operators	p. 52
Dynamical Behaviors in the Limit of Large Confining Lengths and the Appearance of Particle	p. 55
Quantum Time of Arrival Distribution	p. 58
Conclusion	p. 61
References	p. 62
Detector Models for the Quantum Time of Arrival	p. 65
The Time of Arrival in Quantum Mechanics	p. 65
The Basic Atom-Laser Model	p. 70
Complex Potentials	p. 76
Quantum Arrival Times and Operator Normalization	p. 82
Kinetic Energy Densities	p. 87
Disclosing Hidden Information Behind the Quantum Zeno Effect: Pulsed Measurement of the Quantum Time of Arrival	p. 89
Summary	p. 93
References	p. 94
Dwell-Time Distributions in Quantum Mechanics	p. 97
Introduction	p. 97
The Dwell-Time Operator	p. 99
The Free Particle Case	p. 102
The Scattering Case	p. 106
Some Extensions	p. 111
Relation to Flux-Flux Correlation Functions	p. 115
Final Comments	p. 123
References	p. 124
The Quantum Jump Approach and Some of Its Applications	p. 127
Introduction	p. 127
Repeated Measurements on a Single System: Conditional Time Development, Reset Operation, and Quantum Trajectories	p. 129
Application: Macroscopic Light and Dark Periods	p. 141
The General N-Level System and Optical Bloch Equations	p. 145
Quantum Counting Processes	p. 150
How to Replace Density Matrices by Pure States in Simulations	p. 154
Inclusion of Center-of-Mass Motion and Recoil	p. 161
Extension to Spin-Boson Models	p. 165
Discussion	p. 170
References	p. 173
Causality in Superluminal Pulse Propagation	p. 175
Introduction	p. 175
Descriptions of the Velocity of Light Pulses	p. 176
History of Research on Slow and Fast Light	p. 178
The Concept of Simultaneity	p. 185
Causality and Superluminal Pulse Propagation	p. 187
Quantum Mechanical Aspects of Causality and Fast Light	p. 191
Numerical Studies of Propagation Through Fast-Light Media	p. 194
Summary	p. 202
References	p. 202
Experiments on Quantum Transport of Ultra-Cold Atoms in Optical Potentials	p. 205
Introduction	p. 205
Experimental Apparatus	p. 211
Details of the Interaction	p. 212
Quantum Transport	p. 213
Quantum Tunneling	p. 225
Conclusions	p. 236
References	p. 236
Quantum Post-exponential Decay	p. 239
Introduction	p. 239
Simple Models and Examples	p. 247
Three-Dimensional Models of a Particle Escaping from a Confining Potential	p. 252
Physical Interpretation of Post-exponential Decay	p. 258
Toward Experimental Observation	p. 261
Final Comments	p. 271
References	p. 272
Timescales in Quantum Open Systems: Dynamics of Time Correlation Functions and Stochastic Quantum Trajectory Methods in Non-Markovian Systems	p. 277
Introduction	p. 277
Atoms in a Structured Environment, an Example of Non-Markovian Interaction	p. 278
Two Complementary Descriptions of the Dynamics of a Quantum Open System	p. 279
Dynamics of Multiple Time Correlation Functions	p. 284
Examples	p. 291
Discussion and Conclusions	p. 298
References	p. 299
Double-Slit Experiments in the Time Domain	p. 303
Introduction	p. 303
Wave Packet Interference in Position and Momentum Space	p. 304
Time-Domain Double-Slit Experiments	p. 313
Strong-Field Approximation and Interfering Quantum Trajectories	p. 325
References	p. 337
Optimal Time Evolution for Hermitian and Non-Hermitian Hamiltonians	p. 341
Introduction	p. 341
PT Quantum Mechanics	p. 342
Complex Classical Motion	p. 346
Hermitian Quantum Brachistochrone	p. 347
Non-Hermitian Quantum Brachistochrone	p. 354
Extension of Non-Hermitian Hamiltonians to Higher-Dimensional Hermitian Hamiltonians	p. 358
References	p. 360
Atomic Clocks	p. 363
Introduction	p. 363
Why We Need Clocks at All	p. 364
What Is a Clock?	p. 368
How an Atomic Clock Works	p. 369
The "Classic" Caesium Clock	p. 372
The Ramsey Technique	p. 375
Atomic Fountain Clocks	p. 379
Other Types of Atomic Clocks	p. 396
Optical Clocks	p. 402
The Future (Maybe)	p. 407
Precision Tests of Fundamental Theories	p. 409
Conclusion	p. 412
References	p. 412
Index	p. 419
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