Lecture Notes in Physics

By: Robert Alicki, K. Lendi

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Hardcover | 23 April 2007

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Reinvigorated by advances and insights 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. Originally published as Volume 286 (1987) in Lecture in Physics, this volume has been newly typeset, revised and corrected and also expanded to include a review on recent developments.

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General Theory and Applications to Unstable Particles	p. 1
General Theory	p. 1
Introduction	p. 1
Completely Positive Dynamical Semigroups	p. 2
Reduced Dynamics	p. 2
Completely Positive Maps	p. 3
Generalized H-theorem	p. 5
Generators of Quantum Dynamical Semigroups	p. 7
How to Construct Generators?	p. 9
Hamiltonian Models and Markovian Approximation	p. 10
Generalized Master Equation	p. 10
Weak Coupling Limit	p. 11
Low Density Limit	p. 14
Heat Bath, Detailed Balance and Return to Equilibrium	p. 16
Singular Coupling Limit	p. 18
Extensions of the Formalism	p. 19
Nonconservative Dynamical Semigroups	p. 19
Time-dependent Generators	p. 20
Nonlinear Quantum Dynamical Semigroups	p. 21
Discrete Quantum Boltzmann Equation	p. 22
Nonlinear Schrodinger Equation	p. 23
A System of N Two-level Atoms	p. 24
The Hamiltonian of the System	p. 24
The Markovian Master Equation	p. 25
Return to Equilibrium and Superradiance	p. 27
Quantum Dynamical Semigroups for Unstable Particles	p. 29
Introduction	p. 29
Damped and Pumped Quantum Harmonic Oscillator	p. 30
Derivation of the Markovian Master Equation	p. 30
Birth and Death Process, Kinetic Equation	p. 31
Explicit Solutions	p. 31
Models of Unstable Particles	p. 32
Fock Spaces and Quantum Fields	p. 32
Construction of Markovian Master Equation	p. 34
Single-particle Description	p. 35
Explicit Solutions	p. 36
Hamiltonian Models of Unstable Particles	p. 38
Relativistic Unstable Particles	p. 40
Appendix
Banach Spaces B(H) and T(H)	p. 41
One-parameter Semigroups	p. 42
Quantum Correlation Functions	p. 44
References	p. 45
N-Level Systems and Applications to Spectroscopy	p. 47
Introduction	p. 47
General Structure of Quantum Markovian Master Equations for N-level Systems	p. 48
The Kossakowski-Generator of Infinitesimal Time-evolution	p. 48
Positive-semidefiniteness of the Relaxation Matrix	p. 49
Complete Orthonormal Matrix Sets	p. 50
Coherence-vector Formulation	p. 53
Relaxing Semigroups	p. 57
Two-level Systems: Generalized Magnetic or Optical Bloch-equations	p. 61
Details of the Full Relaxation Equations for Static External Fields	p. 61
Alternating External Fields and Constant Relaxation	p. 64
Modified Lineshapes and Free Induction Decay	p. 66
Three-level Systems	p. 69
General Equations	p. 69
Bloch-equations for Decaying Systems	p. 70
Comparison with Common Versions of Master Equations	p. 73
General Considerations	p. 73
Equations for Spontaneous Emission	p. 74
Equations of Lamb-type	p. 76
Open Quantum Systems with Non-constant Relaxation in Time-dependent External Fields	p. 77
Modifications of the Original Semigroup Generator	p. 77
A Model with Field-Strength-dependent Relaxation	p. 79
Determination of Relaxation Parameters from First Principles	p. 81
Relationship between Kossakowski- and Davies-generators	p. 81
A Model for Spin-relaxation by Spin-waves	p. 85
Entropy and Irreversibility	p. 89
Entropy Production	p. 89
Measure of Irreversibility	p. 94
Conclusion	p. 98
Appendix
Generators and Structure Constants for SU(N), N = 2,3,4	p. 99
Eigenvalues of the General Two-level Evolution Matrix	p. 102
Elements of the Time-dependent Two-level Evolution Matrix	p. 104
References	p. 104
Recent Developments	p. 109
Complete Positivity, Entanglement and Decoherence	p. 109
Unbounded Generators and Stochastic Equations	p. 110
Nonlinear QDS	p. 111
Geometry of States and Symmetries of Generators	p. 111
QDS and Thermodynamics	p. 112
Applications in Atomic and Molecular Physics	p. 113
Beyond a Markovian Approximation	p. 114
References	p. 117
Index	p. 123
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Lecture Notes in Physics

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