Open Quantum Systems II: The Markovian ApproachThis 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
Ergodic Properties of Markov Processes | 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 |
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 |
Unitary solutions | 191 |
Regularity | 199 |
Dilation of quantum Markov semigroups | 208 |
Itˆo calculus on Fock space | 93 |
Quantum stochastic calculus | 110 |
The algebra of regular quantum semimartingales | 123 |
Approximation by the toy Fock space | 130 |
Bibliographical comments | 145 |
The right equation with unbounded F | 216 |
Contents of Volume I | 224 |
Contents of Volume III | 232 |
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Open Quantum Systems II: The Markovian Approach Stéphane Attal,Alain Joye,claude-alain pillet Ограниченный просмотр - 2006 |
Часто встречающиеся слова и выражения
algebra applications associated assume Banach space basis bounded bounded operators Brownian motion called classical cocycle compact computation condition consider constant continuous contraction convergence coupling defined definition denote depend dilations distribution domain elements energy ergodic evolution example exists extended finite first Fock space formula function given gives Hamiltonian Hilbert space holds identity implies inequality initial interactions interpretation introduce invariant Italy Lemma limit linear Markov process matrix means measure Moreover natural Note obtain operator particular probabilistic probability problem Proof Proposition prove QSDE quantum dynamical semigroup Quantum Mechanics quantum noises random variable References representation reservoir respect result satisfy semigroup simple solution stationary stochastic differential equations structure Suppose Theorem theory unique unitary vectors