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Books and Monographs
- Quantum Independent Increment Processes II:
Structure of Quantum Lévy Processes, Classical Probability, and Physics, (U. Franz and M. Schürmann, eds.)
- published by Springer-Verlag,
- Barndorff-Nielsen, O.E., Franz, U., Gohm, R., Kümmerer, B., Thorbjørnsen, S.
340 pages, softcover
ISBN-10: 3-540-24407-7
ISBN-13: 978-3-540-24407-3, published 2006
ABOUT THIS BOOK
This is the second of two volumes containing the revised and completed notes of lectures given at the school "Quantum Independent Increment Processes: Structure and Applications to Physics". This school was held at the Alfried-Krupp-Wissenschaftskolleg in Greifswald in March, 2003, and supported by the Volkswagen Foundation. The school gave an introduction to current research on quantum independent increment processes aimed at graduate students and non-specialists working in classical and quantum probability, operator algebras, and mathematical physics.
The present second volume contains the following lectures: "Random Walks on Finite Quantum Groups" by Uwe Franz and Rolf Gohm, "Quantum Markov Processes and Applications in Physics" by Burkhard Kümmerer, Classical and Free Infinite Divisibility and Lévy Processes" by Ole E. Barndorff-Nielsen, Steen Thorbjornsen, and "Lévy Processes on Quantum Groups and Dual Groups" by Uwe Franz.
- Quantum Independent Increment Processes I:
From Classical Probability to Quantum Stochastic Calculus, (U. Franz and M. Schürmann, eds.)
- published by Springer-Verlag,York
- D. Applebaum, B.V.R. Bhat, J. Kustermans, J.M. Lindsay
299 pages, softcover
ISBN-10: 3-540-24406-9
ISBN-13: 978-3-540-24406-6, published 2005
ABOUT THIS BOOK
This volume is the first of two volumes containing the revised and completed notes lectures given at the school "Quantum Independent Increment Processes: Structure and Applications to Physics". This school was held at the Alfried-Krupp-Wissenschaftskolleg in Greifswald during the period March 9 - 22, 2003, and supported by the Volkswagen Foundation. The school gave an introduction to current research on quantum independent increment processes aimed at graduate students and non-specialists working in classical and quantum probability, operator algebras, and mathematical physics.
The present first volume contains the following lectures: "Lévy Processes in Euclidean Spaces and Groups" by David Applebaum, "Locally Compact Quantum Groups" by Johan Kustermans, "Quantum Stochastic Analysis" by J. Martin Lindsay, and "Dilations, Cocycles and Product Systems" by B.V. Rajarama Bhat.
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- Quantum Theory and Its Stochastic Limit
- published by Springer-Verlag, New York
- Editors: Luigi Accardi, University of Rome, Italy, Yun Gang Lu, University of Bari, Italy, Igor Volovich, Steklov Mathematical Institute, Moscow, Russia
493 pages 518 illus., hardcover
ISBN: 3-540-41928-4, published 2002
ABOUT THIS BOOK
The subject of this book is a new mathematical technique, the stochastic limit developed for solving nonlinear problems in quantum theory involving systems with infinitely many degrees of freedom (typically quantum fields or gases in the thermodynamic limit). This technique is condensed into some easily applied rules (called "stochastic golden rules") which allow us to single out the dominating contributions to the dynamical evolution of systems in regimes involving long times and small effects. In the stochastic limit the original Hamiltonian theory is approximated using a new Hamiltonian theory which is singular. These singular Hamiltonians still define a unitary evolution and the new equations give much more insight into the relevant physical phenomena than the original Hamiltonian equations. Especially, one can explicitly compute multi-time correlations (e.g. photon statistics) or coherent vectors, which are beyond the reach of typical asymptotic techniques.
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Contact
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Copyright © Association for Quantum Probability and Infinite Dimensional Analysis (AQPIDA)
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