Attal / Joye / Pillet Open Quantum Systems III

Recent Developments
1. Auflage 2006
ISBN: 978-3-540-33967-0
Verlag: Springer Berlin Heidelberg
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 1882, 326 Seiten

Reihe: Lecture Notes in Mathematics

Understanding dissipative dynamics of open quantum systems remains a challenge in mathematical physics. This problem is relevant in various areas of fundamental and applied physics. From a mathematical point of view, it involves a large body of knowledge. Significant progresses in the understanding of such systems have been made during the last decade. These books present in a self-contained way the mathematical theories involved in the modelization of such phenomena. They describe physically relevant models, develop their mathematical analysis and derive their physical implications.

In "Volume I" the Hamiltonian description of quantum open systems is discussed. This includes an introduction to quantum statistical mechanics and its operator algebraic formulation, modular theory, spectral analysis and their applications to quantum dynamical systems.

"Volume II" is dedicated to the Markovian formalism of classical and quantum open systems. A complete exposition of noise theory, Markov processes and stochastic differential equations, both in the classical and the quantum context, is provided. These mathematical tools are put into perspective with physical motivations and applications.

"Volume III" is devoted to recent developments and applications. The topics discussed include the non-equilibrium properties of open quantum systems, the Fermi Golden Rule and weak coupling limit, quantum irreversibility and decoherence, qualitative behaviour of quantum Markov semigroups and continual quantum measurements.

Autoren/Hrsg.

Attal, Stéphane

Joye, Alain

Pillet, Claude-Alain

Inhaltsverzeichnis

1;Preface;5
2;Contents;8
3;List of Contributors;13
4;Topics in Non-Equilibrium Quantum Statistical Mechanics;15
4.1;1 Introduction;16
4.2;2 Conceptual Framework;17
4.3;3 Mathematical Framework;19
4.4;4 Open Quantum Systems;28
4.5;5 Free Fermi Gas Reservoir;40
4.6;6 The Simple Electronic Black-Box (SEBB) Model;48
4.7;7 Thermodynamics of the SEBB Model;57
4.8;8 FGR Thermodynamics of the SEBB Model;64
4.9;9 Appendix;72
4.10;References;77
5;Fermi Golden Rule and Open Quantum Systems;81
5.1;1 Introduction;82
5.2;2 Fermi Golden Rule in an Abstract Setting;85
5.3;3 Weak Coupling Limit;91
5.4;4 Completely Positive Semigroups;102
5.5;5 Small Quantum System Interacting with Reservoir;107
5.6;6 Two Applications of the Fermi Golden Rule to Open Quantum;111
5.7;Systems;111
5.8;7 Fermi Golden Rule for a Composite Reservoir;122
5.9;A Appendix – One-Parameter Semigroups;126
5.10;References;129
6;Decoherence as Irreversible Dynamical Process in Open Quantum Systems;131
6.1;1 Physical and Mathematical Prologue;132
6.2;2 The Asymptotic Decomposition of T;140
6.3;3 Review of Decoherence Effects in Infinite Spin Systems;152
6.4;4 Dynamical Semigroups on CCR Algebras;162
6.5;5 Outlook;171
6.6;Acknowledgements;172
6.7;References;172
7;Notes on the Qualitative Behaviour of Quantum Markov Semigroups*;174
7.1;1 Introduction;175
7.2;2 Ergodic Theorems;178
7.3;3 The Minimal Quantum Dynamical Semigroup;180
7.4;4 The Existence of Stationary States;185
7.5;5 Faithful Stationary States and Irreducibility;197
7.6;6 The Convergence Towards the Equilibrium;202
7.7;7 Recurrence and Transience of Quantum Markov Semigroups;207
7.8;References;216
8;Continual Measurements in Quantum Mechanics and Quantum Stochastic Calculus;219
8.1;1 Introduction;220
8.2;2 Unitary Evolution and States;222
8.3;3 Continual Measurements;242
8.4;4 A Three–Level Atom and the Shelving Effect;270
8.5;5 A Two–Level Atom and the Spectrum of the Fluorescence;281
8.6;Light;281
8.7;Acknowledgments;300
8.8;References;300
9;Index of Volume III;305
10;Information About the Other Two Volumes;309
10.1;Contents of Volume I;310
10.2;Index of Volume I;314
10.3;Contents of Volume II;318
10.4;Index of Volume II;321