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Open Quantum Systems I: The Hamiltonian Approach (Lecture Notes in Mathematics)
 
 
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Open Quantum Systems I: The Hamiltonian Approach (Lecture Notes in Mathematics) [Paperback]

Stéphane Attal (Editor), Alain Joye (Editor), Claude-Alain Pillet (Editor)

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Book Description

July 26, 2006 3540309918 978-3540309918 1

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. Significant progress in the understanding of such systems has been made recently. These books present the mathematical theories involved in the modeling of such phenomena. They describe physically relevant models, develop their mathematical analysis and derive their physical implications.


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Open Quantum Systems I: The Hamiltonian Approach (Lecture Notes in Mathematics) + Open Quantum Systems II: The Markovian Approach (Lecture Notes in Mathematics) + Open Quantum Systems III: Recent Developments (Lecture Notes in Mathematics)
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From the Back Cover

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 progress in the understanding of such systems has been made during the last decade. These books present in a self-contained way the mathematical theories involved in the modeling 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.


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Inside This Book (learn more)
Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
standard vector representative, quantum dynamical system, normal invariant state, rank one perturbations, momentum density distribution, finite quantum systems, spectral averaging, open quantum systems, strongly continuous group, deficiency indices, mean ergodic theorem, singular continuous spectrum, test function space, spectral theorem, cyclic subspace, nonzero density, spectral subspaces, covering lemma, analytic vectors, relative bound, cyclic vector, spectral measure, essential range, vacuum vector, functional calculus
Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, Academic Press, Koopman-von Neumann, Methods of Modern Mathematical Physics, Classical Mechanics, Cambridge University Press, Prove Relation, The Hardy, Large Coulomb, Prove Proposition, Springer Verlag
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