Quantum Potential Theory

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.

List of contents

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.

Summary

This book offers the revised and completed notes of lectures given at the 2007 conference, "Quantum Potential Theory: Structures and Applications to Physics." These lectures provide an introduction to the theory and discuss various applications.

Product details

• Authors: Philipp Biane, Philippe Biane, Lu Bouten, Luc Bouten, Fabio Cipriani, Fabio et al Cipriani, Norio Konno, Nicolas Privault, Quanhua Xu
• Assisted by: Uw Franz (Editor), Uwe Franz (Editor), Uwe (Hrsg.) Franz (Editor), Schuermann (Editor), Schuermann (Editor), Michael Schuermann (Editor), Michael Schürmann (Editor), Michael (Hrsg.) Schürmann (Editor)
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 01.01.2008
• EAN: 9783540693642
• ISBN: 978-3-540-69364-2
• No. of pages: 464
• Illustrations: 18 SW-Abb.
• Series: Lecture Notes in Mathematics; (1954) Lecture Notes in Mathematics; Lecture Notes in Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Analysis; B, Mathematics and Statistics, Quantum Physics, Differential Geometry, Quantum physics (quantum mechanics & quantum field theory), Manifolds (Mathematics), Stochastics, Quantum computers, Global analysis (Mathematics), Global Analysis and Analysis on Manifolds, Differential & Riemannian geometry, Potential Theory, Potential theory (Mathematics), Spintronics, Quantum Information Technology, Spintronics