Biane, Philippe.
Quantum Potential Theory [electronic resource] / by Philippe Biane, Luc Bouten, Fabio Cipriani, Norio Konno, Nicolas Privault, Quanhua Xu ; edited by Uwe Franz, Michael Schürmann. - Berlin, Heidelberg : Springer Berlin Heidelberg, 2008. - online resource. - Lecture Notes in Mathematics, 1954 0075-8434 ; . - Lecture Notes in Mathematics, 1954 .
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.
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, i.e. 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.
9783540693659
10.1007/978-3-540-69365-9 doi
Mathematics.
Global analysis.
Potential theory (Mathematics).
Global differential geometry.
Quantum computing.
Mathematics.
Global Analysis and Analysis on Manifolds.
Quantum Computing, Information and Physics.
Differential Geometry.
Potential Theory.
QA614-614.97
514.74
Quantum Potential Theory [electronic resource] / by Philippe Biane, Luc Bouten, Fabio Cipriani, Norio Konno, Nicolas Privault, Quanhua Xu ; edited by Uwe Franz, Michael Schürmann. - Berlin, Heidelberg : Springer Berlin Heidelberg, 2008. - online resource. - Lecture Notes in Mathematics, 1954 0075-8434 ; . - Lecture Notes in Mathematics, 1954 .
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.
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, i.e. 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.
9783540693659
10.1007/978-3-540-69365-9 doi
Mathematics.
Global analysis.
Potential theory (Mathematics).
Global differential geometry.
Quantum computing.
Mathematics.
Global Analysis and Analysis on Manifolds.
Quantum Computing, Information and Physics.
Differential Geometry.
Potential Theory.
QA614-614.97
514.74