| 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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