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The Theory of Open Quantum Systems$
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Heinz-Peter Breuer and Francesco Petruccione

Print publication date: 2007

Print ISBN-13: 9780199213900

Published to Oxford Scholarship Online: January 2010

DOI: 10.1093/acprof:oso/9780199213900.001.0001

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Quantum Master Equations

Quantum Master Equations

The Theory of Open Quantum Systems

Heinz-Peter Breuer

Francesco Petruccione

Oxford University Press

This chapter introduces the fundamentals of the description of the quantum dynamics of open systems in terms of quantum master equations, together with its most important applications. Special emphasis is laid on the theory of completely positive quantum dynamical semigroups, which leads to the concept of a quantum Markov process. It discusses the relaxation to equilibrium and the multi-time structure of quantum Markov processes, as well as their irreversible nature which is characterized by an appropriate entropy functional. Microscopic derivations for various quantum master equations are presented, such as the quantum optical master equation and the master equation for quantum Brownian motion. As a further application, the master equation describing continuous measurements is derived and used to study the quantum Zeno effect. The chapter also contains a treatment of non-linear, mean field quantum master equations together with applications to laser theory and super-radiance.

Keywords:   quantum Markov processes, master equations, continuous measurements, quantum zeno effect, quantum Brownian motion, nonlinear master equations

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