Quantum Potential Theory

• Main Authors: Biane, Philippe (Author), Bouten, Luc (Author), Cipriani, Fabio (Author), Konno, Norio (Author), Privault, Nicolas (Author), Xu, Quanhua (Author)
• Corporate Author: SpringerLink (Online service)
• Other Authors: Franz, Uwe (Editor), Schürmann, Michael (Editor)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2008.
• Series: Lecture Notes in Mathematics, 1954
• Subjects: Mathematics.; Global analysis (Mathematics).; Manifolds (Mathematics).; Potential theory (Mathematics).; Differential geometry.; Quantum physics.; Quantum computers.; Spintronics.; Global Analysis and Analysis on Manifolds.; Quantum Physics.; Quantum Information Technology, Spintronics.; Differential Geometry.; Potential Theory.
• Physical Description: XII, 464 p. 18 illus. online resource.
• ISBN: 9783540693659
• ISSN: 0075-8434 ;

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.