The Theory of Open Quantum Systems by Heinz-Peter Breuer

The Theory of Open Quantum Systems

byHeinz-Peter Breuer, Francesco Petruccione

Paperback | February 25, 2007

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This book treats the central physical concepts and mathematical techniques used to investigate the dynamics of open quantum systems. To provide a self-contained presentation the text begins with a survey of classical probability theory and with an introduction into the foundations of quantummechanics with particular emphasis on its statistical interpretation. The fundamentals of density matrix theory, quantum Markov processes and dynamical semigroups are developed. The most important master equations used in quantum optics and in the theory of quantum Brownian motion are applied to thestudy of many examples. Special attention is paid to the theory of environment induced decoherence, its role in the dynamical description of the measurement process and to the experimental observation of decohering Schrodinger cat states.The book includes the modern formulation of open quantum systems in terms of stochastic processes in Hilbert space. Stochastic wave function methods and Monte Carlo algorithms are designed and applied to important examples from quantum optics and atomic physics, such as Levy statistics in the lasercooling of atoms, and the damped Jaynes-Cummings model. The basic features of the non-Markovian quantum behaviour of open systems are examined on the basis of projection operator techniques. In addition, the book expounds the relativistic theory of quantum measurements and discusses several examplesfrom a unified perspective, e.g. non-local measurements and quantum teleportation. Influence functional and super-operator techniques are employed to study the density matrix theory in quantum electrodynamics and applications to the destruction of quantum coherence are presented.The text addresses graduate students and lecturers in physics and applied mathematics, as well as researchers with interests in fundamental questions in quantum mechanics and its applications. Many analytical methods and computer simulation techniques are developed and illustrated with the help ofnumerous specific examples. Only a basic understanding of quantum mechanics and of elementary concepts of probability theory is assumed.

About The Author

PD Dr. Heinz-Peter Breuer, Physikalisches Institut, Albert-Ludwigs-Universitaet, Freiburg, Germany. Professor Francesco Petruccione, School of Pure and Applied Physics, University of KwaZulu-Natal, Durban, South Africa.

Details & Specs

Title:The Theory of Open Quantum SystemsFormat:PaperbackDimensions:656 pages, 9.21 × 6.14 × 1.26 inPublished:February 25, 2007Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0199213909

ISBN - 13:9780199213900

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Table of Contents

PrefaceAcknowledgementsPart 1: Probability in Classical and Quantum Physics1. Classical probability theory and stochastic processes2. Quantum ProbabilityPart 2: Density Matrix Theory3. Quantum Master Equations4. DecoherencePart 3: Stochastic Processes in Hilbert Space5. Probability distributions on Hilbert space6. Stochastic dynamics in Hilbert space7. The stochastic simulation method8. Applications to quantum optical systemsPart 4: Non-Markovian Quantum Processes9. Projection operator techniques10. Non-Markovian dynamics in physical systemsPart 5: Relativistic Quantum Processes11. Measurements in relativistic quantum mechanics12. Open quantum electrodynamics

Editorial Reviews

`'This book covers a large set of topics, normally not covered in standard physics curricula ... I recommend this book to physicists interested in widening their horizons in the directions covered by the book ... I do not know of any other source providing such a systematic and well writtenintroduction into this area of research.''Mathematical Reviews