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9783540244073

Quantum Independent Increment Processes II : Structure of Quantum Levy Processes, Classical Probability, and Physics

by ; ; ; ;
  • ISBN13:

    9783540244073

  • ISBN10:

    3540244077

  • Format: Paperback
  • Copyright: 2006-01-30
  • Publisher: Springer Verlag
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Summary

"This series reports on new developments in mathematical research and teaching - quickly, informally and at a high level. The type of material considered for publication includes: research monographs; lectures on a new field or presentations of a new angle in a classical field; and summer schools and intensive courses on topics of current research."--BOOK JACKET.

Table of Contents

Random Walks on Finite Quantum Groups
Uwe Franz, Rolf Gohm
1(32)
1 Markov Chains and Random Walks in Classical Probability
3(2)
2 Quantum Markov Chains
5(2)
3 Random Walks on Comodule Algebras
7(4)
4 Random Walks on Finite Quantum Groups
11(1)
5 Spatial Implementation
12(6)
6 Classical Versions
18(4)
7 Asymptotic Behavior
22(2)
A Finite Quantum Groups
24(2)
B The Eight-Dimensional Kac-Paljutkin Quantum Group
26(4)
References
30(3)
Classical and Free Infinite Divisibility and Lévy Processes
Ole E. Barndorff-Nielsen, Steen Thorbjørnsen
33(128)
1 Introduction
34(1)
2 Classical Infinite Divisibility and Levy Processes
35(13)
3 Upsilon Mappings
48(44)
4 Free Infinite Divisibility and Lévy Processes
92(21)
5 Connections between Free and Classical Infinite Divisibility
113(10)
6 Free Stochastic Integration
123(27)
A Unbounded Operators Affiliated with a W*-Probability Space
150(5)
References
155(6)
Lévy Processes on Quantum Groups and Dual Groups
Uwe Franz
161(98)
1 Lévy Processes on Quantum Groups
163(21)
2 Lévy Processes and Dilations of Completely Positive Semigroups
184(14)
3 The Five Universal Independences
198(31)
4 Lévy Processes on Dual Groups
229(25)
References
254(5)
Quantum Markov Processes and Applications in Physics
Burkhard Kümmerer
259(72)
1 Quantum Mechanics
262(3)
2 Unified Description of Classical and Quantum Systems
265(3)
3 Towards Markov Processes
268(13)
4 Scattering for Markov Processes
281(13)
5 Markov Processes in the Physics Literature
294(3)
6 An Example on M2
297(5)
7 The Micro-Maser as a Quantum Markov Process
302(6)
8 Completely Positive Operators
308(4)
9 Semigroups of Completely Positive Operators and Lindblad Generators
312(3)
10 Repeated Measurement and its Ergodic Theory
315(13)
References
328(3)
Index 331

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