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Quantum dynamical semigroups and applications

Author: R Alicki; Karl Lendi
Publisher: Berlin ; New York : Springer, ©2007.
Series: Lecture notes in physics, 717.
Edition/Format:   Print book : English : [2nd rev., corr. and expanded ed.]View all editions and formats
Database:WorldCat
Summary:

Reinvigorated by advances and insights the quantum theory of irreversible processes has recently attracted growing attention. Originally published as Volume 286 (1987) in Lecture in Physics, this  Read more...

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: R Alicki; Karl Lendi
ISBN: 9783540708605 354070860X 0387182764 9780387182766
OCLC Number: 123893602
Notes: Originally published in 1987 as vol. 286 of Lecture notes in physics.
Description: xi, 128 pages ; 24 cm.
Contents: General Theory and Applications to Unstable Particles / Robert Alicki 1 --
1 General Theory 1 --
1.2 Completely Positive Dynamical Semigroups 2 --
1.2.1 Reduced Dynamics 2 --
1.2.2 Completely Positive Maps 3 --
1.2.3 Generalized H-theorem 5 --
1.2.4 Generators of Quantum Dynamical Semigroups 7 --
1.2.5 How to Construct Generators? 9 --
1.3 Hamiltonian Models and Markovian Approximation 10 --
1.3.1 Generalized Master Equation 10 --
1.3.2 Weak Coupling Limit 11 --
1.3.3 Low Density Limit 14 --
1.3.4 Heat Bath, Detailed Balance and Return to Equilibrium 16 --
1.3.5 Singular Coupling Limit 18 --
1.4 Extensions of the Formalism 19 --
1.4.1 Nonconservative Dynamical Semigroups 19 --
1.4.2 Time-dependent Generators 20 --
1.4.3 Nonlinear Quantum Dynamical Semigroups 21 --
1.4.4 Discrete Quantum Boltzmann Equation 22 --
1.4.5 Nonlinear Schrodinger Equation 23 --
1.5 A System of N Two-level Atoms 24 --
1.5.1 The Hamiltonian of the System 24 --
1.5.2 The Markovian Master Equation 25 --
1.5.3 Return to Equilibrium and Superradiance 27 --
2 Quantum Dynamical Semigroups for Unstable Particles 29 --
2.2 Damped and Pumped Quantum Harmonic Oscillator 30 --
2.2.1 Derivation of the Markovian Master Equation 30 --
2.2.2 Birth and Death Process, Kinetic Equation 31 --
2.2.3 Explicit Solutions 31 --
2.3 Models of Unstable Particles 32 --
2.3.1 Fock Spaces and Quantum Fields 32 --
2.3.2 Construction of Markovian Master Equation 34 --
2.3.3 Single-particle Description 35 --
2.3.4 Explicit Solutions 36 --
2.3.5 Hamiltonian Models of Unstable Particles 38 --
2.3.6 Relativistic Unstable Particles 40 --
A.1 Banach Spaces B(H) and T(H) 41 --
A.2 One-parameter Semigroups 42 --
A.3 Quantum Correlation Functions 44 --
N-Level Systems and Applications to Spectroscopy / Karl Lendi 47 --
2 General Structure of Quantum Markovian Master Equations for N-level Systems 48 --
2.1 The Kossakowski-Generator of Infinitesimal Time-evolution 48 --
2.2 Positive-semidefiniteness of the Relaxation Matrix 49 --
2.3 Complete Orthonormal Matrix Sets 50 --
2.4 Coherence-vector Formulation 53 --
2.5 Relaxing Semigroups 57 --
3 Two-level Systems: Generalized Magnetic or Optical Bloch-equations 61 --
3.1 Details of the Full Relaxation Equations for Static External Fields 61 --
3.2 Alternating External Fields and Constant Relaxation 64 --
3.3 Modified Lineshapes and Free Induction Decay 66 --
4 Three-level Systems 69 --
4.1 General Equations 69 --
4.2 Bloch-equations for Decaying Systems 70 --
5 Comparison with Common Versions of Master Equations 73 --
5.2 Equations for Spontaneous Emission 74 --
5.3 Equations of Lamb-type 76 --
6 Open Quantum Systems with Non-constant Relaxation in Time-dependent External Fields 77 --
6.1 Modifications of the Original Semigroup Generator 77 --
6.2 A Model with Field-Strength-dependent Relaxation 79 --
7 Determination of Relaxation Parameters from First Principles 81 --
7.1 Relationship between Kossakowski- and Davies-generators 81 --
7.2 A Model for Spin-relaxation by Spin-waves 85 --
8 Entropy and Irreversibility 89 --
8.1 Entropy Production 89 --
8.2 Measure of Irreversibility 94 --
A.1 Generators and Structure Constants for SU(N), N = 2,3,4 99 --
A.2 Eigenvalues of the General Two-level Evolution Matrix 102 --
A.3 Elements of the Time-dependent Two-level Evolution Matrix 104 --
Recent Developments / Robert Alicki, Karl Lendi 109 --
1 Complete Positivity, Entanglement and Decoherence 109 --
2 Unbounded Generators and Stochastic Equations 110 --
3 Nonlinear QDS 111 --
4 Geometry of States and Symmetries of Generators 111 --
5 QDS and Thermodynamics 112 --
6 Applications in Atomic and Molecular Physics 113 --
7 Beyond a Markovian Approximation 114.
Series Title: Lecture notes in physics, 717.
Responsibility: Robert Alicki, Karl Lendi.

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