Quantum Probability and Applications III: Proceedings of a Conference held in Oberwolfach, FRG, January 25–31, 1987

Luigi Accardi (auth.), Luigi Accardi, Wilhelm von Waldenfels (eds.)354018919X, 9783540189190, 038718919X

These proceedings of the first Quantum Probability meeting held in Oberwolfach is the fourth in a series begun with the 1982 meeting of Mondragone and continued in Heidelberg (’84) and in Leuven (’85). The main topics discussed were: quantum stochastic calculus, mathematical models of quantum noise and their applications to quantum optics, the quantum Feynman-Kac formula, quantum probability and models of quantum statistical mechanics, the notion of conditioning in quantum probability and related problems (dilations, quantum Markov processes), quantum central limit theorems. With the exception of Kümmerer’s review article on Quantum Markov Processes, all contributions are original research papers.

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Table of contents :
A note on Meyer’s note….Pages 1-5
Stochastic integration….Pages 6-19
Quantum stochastic parallel transport on non-commutative vector bundles….Pages 20-36
Input and output channels in quantum systems and quantum stochastic differential equations….Pages 37-51
Some noncommutative Radon-Nikodym Theorems for von Neumann algebras….Pages 52-68
Multidimensional quantum diffusions….Pages 69-88
An application of de finetti’s theorem….Pages 89-102
The quantum Langevin equation from the independent-oscillator model….Pages 103-106
Quantum poisson processes: Physical motivations and applications….Pages 107-127
A noncommutative generalization of conditionally positive definite functions….Pages 128-148
Contraction semigroups in L 2 over a von neumann algebra….Pages 149-153
Survey on a theory of non-commutative stationary markov processes….Pages 154-182
Dynamical entropy for quantum systems….Pages 183-191
An integral kernel approach to noise….Pages 192-208
A note on shifts and cocycles….Pages 209-212
Local measures in fock space stochastic calculus and a generalized ito-tanaka formula….Pages 213-231
Representation of a class of quantum martingales II….Pages 232-250
Conditional expectation in quantum probability….Pages 251-260
Mutual quadratic variation and ito’s table in quantum stochastic calculus….Pages 261-274
On mixing properties of automorphisms of von neumann algebras related to measure space transformations….Pages 275-284
First exit time: A theory of stopping times in quantum processes….Pages 285-299
A central limit theorem on the free lie group….Pages 300-318
Entropy, observability and the generalised second law of thermodynamics….Pages 319-328
Remarks on asymptotic properties of groups of the bogoliubov transformations of car c*-algebras….Pages 329-342
Linear and non-linear stochastic processes….Pages 343-353
Detailed balance and critical slowing down….Pages 354-362
Quantum martingales and stochastic integrals….Pages 363-373