Quantum Potential Theory [electronic resource] / by Philippe Biane, Luc Bouten, Fabio Cipriani, Norio Konno, Nicolas Privault, Quanhua Xu ; edited by Uwe Franz, Michael Schürmann.

Biane, P. (Philippe) author., Author,
Berlin, Heidelberg : Springer Berlin Heidelberg, 2008.
Lecture Notes in Mathematics, 0075-8434 ; 1954
Lecture Notes in Mathematics, 0075-8434 ; 1954
1 online resource (XII, 464 pages 18 illustrations)
Global analysis.
Quantum theory.
Global differential geometry.
Potential theory (Mathematics).
Local subjects:
Global Analysis and Analysis on Manifolds.
Quantum Physics.
Quantum Information Technology, Spintronics.
Differential Geometry.
Potential Theory.
System Details:
text file PDF
This volume contains the revised and completed notes of lectures given at the school "Quantum Potential Theory: Structure and Applications to Physics," held at the Alfried-Krupp-Wissenschaftskolleg in Greifswald from February 26 to March 10, 2007. Quantum potential theory studies noncommutative (or quantum) analogs of classical potential theory. These lectures provide an introduction to this theory, concentrating on probabilistic potential theory and it quantum analogs, id est quantum Markov processes and semigroups, quantum random walks, Dirichlet forms on C* and von Neumann algebras, and boundary theory. Applications to quantum physics, in particular the filtering problem in quantum optics, are also presented.
Potential Theory in Classical Probability
to Random Walks on Noncommutative Spaces
Interactions between Quantum Probability and Operator Space Theory
Dirichlet Forms on Noncommutative Spaces
Applications of Quantum Stochastic Processes in Quantum Optics
Quantum Walks.
Bouten, Luc. author., Author,
Cipriani, Fabio. author., Author,
Konno, Norio, author., Author,
Privault, Nicolas. author., Author,
Xu, Quanhua. author., Author,
Franz, Uwe, editor., Editor,
Schürmann, Michael. editor., Editor,
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Publisher Number:
10.1007/978-3-540-69365-9 doi
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