Quantum Dynamical Semigroups and Applications

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Springer Science & Business Media, 23 апр. 2007 г. - Всего страниц: 129

Reinvigorated by advances and insights, in particular from the active fields of quantum information and computing, the quantum theory of irreversible processes has recently attracted growing attention.

This volume introduces the very basic concepts of semigroup dynamics of open quantum systems and reviews a variety of modern applications. The present book, originally published as Vol. 286 (1987) in Lecture in Physics, has been newly typeset, revised and corrected and also expanded to include a review on recent developments.

 

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Содержание

General Theory and Applications to Unstable Particles
1
12 Completely Positive Dynamical Semigroups
2
122 Completely Positive Maps
3
123 Generalized Htheorem
5
124 Generators of Quantum Dynamical Semigroups
7
125 How to Construct Generators?
9
13 Hamiltonian Models and Markovian Approximation
10
133 Low Density Limit
14
2 General Structure of Quantum Markovian Master Equations for Nlevel Systems
48
22 Positivesemidefiniteness of the Relaxation Matrix
49
23 Complete Orthonormal Matrix Sets
50
24 Coherencevector Formulation
53
25 Relaxing Semigroups
57
Generalized Magnetic or Optical Blochequations
61
32 Alternating External Fields and Constant Relaxation
64
33 Modified Lineshapes and Free Induction Decay
66

134 Heat Bath Detailed Balance and Return to Equilibrium
16
135 Singular Coupling Limit
18
14 Extensions of the Formalism
19
142 Timedependent Generators
20
143 Nonlinear Quantum Dynamical Semigroups
21
144 Discrete Quantum Boltzmann Equation
22
145 Nonlinear Schrodinger Equation
23
15 A System of N Twolevel Atoms
24
152 The Markovian Master Equation
25
153 Return to Equilibrium and Superradiance
27
2 Quantum Dynamical Semigroups for Unstable Particles
29
22 Damped and Pumped Quantum Harmonic Oscillator
30
222 Birth and Death Process Kinetic Equation
31
23 Models of Unstable Particles
32
232 Construction of Markovian Master Equation
34
233 Singleparticle Description
35
234 Explicit Solutions
36
235 Hamiltonian Models of Unstable Particles
38
236 Relativistic Unstable Particles
40
A1 Banach Spaces BH and TH
41
A2 Oneparameter Semigroups
42
A3 Quantum Correlation Functions
44
References
45
NLevel Systems and Applications to Spectroscopy
47
4 Threelevel Systems
69
42 Blochequations for Decaying Systems
70
5 Comparison with Common Versions of Master Equations
73
52 Equations for Spontaneous Emission
74
53 Equations of Lambtype
76
6 Open Quantum Systems with Nonconstant Relaxation in Timedependent External Fields
77
62 A Model with FieldStrengthdependent Relaxation
79
7 Determination of Relaxation Parameters from First Principles
81
72 A Model for Spinrelaxation by Spinwaves
85
8 Entropy and Irreversibility
89
82 Measure of Irreversibility
94
9 Conclusion
98
Appendix
99
A2 Eigenvalues of the General Twolevel Evolution Matrix
102
A3 Elements of the Timedependent Twolevel Evolution Matrix
104
Recent Developments
108
2 Unbounded Generators and Stochastic Equations
110
3 Nonlinear QDS
111
5 QDS and Thermodynamics
112
6 Applications in Atomic and Molecular Physics
113
7 Beyond a Markovian Approximation
114
References
117
Index
123
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