Open Quantum Systems II: The Markovian Approach

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Stéphane Attal, Alain Joye, claude-alain pillet
Springer, 29 авг. 2006 г. - Всего страниц: 244
This volume is the second in a series of three volumes dedicated to the lecture notes of the summer school “Open Quantum Systems” which took place in the Institut Fourier in Grenoble, from June 16th to July 4th 2003. The contributions presented in thesevolumesarerevisedandexpandedversionsofthenotesprovidedtothestudents during the school. After the rst volume, developing the Hamiltonian approach of open quantum systems, this second volume is dedicated to the Markovian approach. The third volume presents both approaches, but at the recent research level. Open quantum systems A quantum open system is a quantum system which is interacting with another one. This is a general de nition, but in general, it is understood that one of the s- tems is rather “small” or “simple” compared to the other one which is supposed to be huge, to be the environment, a gas of particles, a beam of photons, a heat bath ... The aim of quantum open system theory is to study the behaviour of this coupled system and in particular the dissipation of the small system in favour of the large one.
 

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Содержание

Contents
1
Brownian Motion
12
Control Theory and Irreducibility
24
References
39
the chain
52
Heat Flow and Entropy Production
66
References
77
Quantum Noises
79
Approximation by the toy Fock space
130
Bibliographical comments
145
Completely positive maps
157
Dilations of CP and CB maps
163
Dilations of quantum Markov semigroups
173
References
181
Quantum Stochastic Differential Equations and Dilation of Completely
183
Cocycle property
196

Ito calculus on Fock space
93
Quantum stochastic calculus
110
The algebra of regular quantum semimartingales
123

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