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El. knyga: Mathematics Of Open Quantum Systems, The: Dissipative And Non-unitary Representations And Quantum Measurements

(Niagara Univ, Usa), (Univ Of Missouri, Usa)
  • Formatas: 300 pages
  • Išleidimo metai: 24-Dec-2021
  • Leidėjas: World Scientific Publishing Co Pte Ltd
  • Kalba: eng
  • ISBN-13: 9789811241246
  • Formatas: 300 pages
  • Išleidimo metai: 24-Dec-2021
  • Leidėjas: World Scientific Publishing Co Pte Ltd
  • Kalba: eng
  • ISBN-13: 9789811241246

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The authors provide a mathematical framework that details the results of continuous observation of quantum systems, focusing on the idea that a quantum observation always impacts the system subject to it and that the initial system should be seen as an open system that interacts with part of the larger system. They address the simplest dissipative solutions of the Heisenberg commutation relations based on the study of unitary invariants of symmetric operators, then mathematical problems of continuous monitoring of general quantum systems prepared in a pure state, with emphasis on the behavior of massless particles on a ring under continuous monitoring. Annotation ©2022 Ringgold, Inc., Portland, OR (protoview.com)
Acknowledgments vii
Preface ix
Part 1 Representations of Operator Commutation Relations
2(117)
1 Introduction
3(10)
2 Preliminaries and Basic Definitions
13(6)
3 The Commutation Relations and Character-Automorphic Functions
19(10)
4 The Differentiation Operator on Metric Graphs
29(8)
5 The Magnetic Hamiltonian
37(12)
6 The Livsic Function S(D, De)(z)
49(8)
7 The Weyl-Titchmarsh Function M(D, D)(z)
57(8)
8 The Model Dissipative Operators
65(8)
9 The Characteristic Function S(D, D, De)(z)
73(8)
10 The Transmission Coefficient and the Characteristic Function
81(6)
11 Uniqueness Results
87(6)
12 Dissipative Solutions to the CCR
93(4)
13 Main Results
97(18)
14 Unitary Dynamics on the Full Graph
115(4)
Part 2 Continuous Monitoring, Quantum Measurements
119(102)
15 Continuous Monitoring of the Quantum Systems
121(16)
15.1 Quantum Zeno Effect
122(1)
15.2 Anti-Zeno Effect
123(2)
15.3 The Exponential Decay
125(5)
15.4 Frequent Measurements and the Time-Energy Uncertainty Principle
130(1)
15.5 Presto
131(6)
16 The Quantum Zeno versus Anti-zeno Effect Alternative
137(18)
17 The Quantum Zeno Effect versus Exponential Decay Alternative
155(22)
18 Preliminaries: Probabilities versus Amplitudes
177(2)
19 Massless Particles on a Ring
179(2)
20 Continuous Monitoring with Interference
181(8)
20.1 Discussion
184(5)
21 Continuous Monitoring with No Interference
189(6)
21.1 Discussion
191(4)
22 The Self-adjoint Dilation
195(6)
23 General Open Quantum Systems on a Ring
201(10)
23.1 Discussion
207(1)
23.2 Random Phase Method
208(3)
24 Operator Coupling Limit Theorems
211(10)
Appendix A The Characteristic Function for Rank-One Perturbations 221(8)
Appendix B Prime Symmetric Operators 229(8)
Appendix C A Functional Model of a Triple 237(4)
Appendix D The Spectral Analysis of the Model Dissipative Operator 241(8)
Appendix E Transformation Laws 249(8)
Appendix F The Invariance Principle 257(6)
Appendix G The Operator Coupling and the Multiplication Theorem 263(6)
Appendix H Stable Laws 269(4)
References 273(10)
Index 283