Quantum potential theory /

Quantum potential theory /

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Bibliographic Details
Imprint:Berlin : Springer, c2008.
Description:xi, 457 p. : ill. ; 24 cm.
Language:English
Series:Lecture notes in mathematics, 0075-8434 ; 1954
Lecture notes in mathematics (Springer-Verlag) ; 1954.
Subject:
Potential theory (Mathematics)
Markov processes.
Semigroups.
Functional analysis.
Functional analysis.
Markov processes.
Potential theory (Mathematics)
Semigroups.
Format: Print Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/7363423
Hidden Bibliographic Details
Other authors / contributors:Schürmann, Michael. 1955-
Franz, Uwe.
Privault, Nicolas.
Biane, P. (Philippe)
Xu, Quanhua.
Cipriani, Fabio.
Bouten, Luc.
Konno, Norio.
ISBN:9783540693642 (softcover)
3540693645 (softcover)
Notes:"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" - p. [4] of cover.
Includes bibliographical references and index.
Table of Contents:
  • Introduction
  • Potential Theory in Classical Probability
  • 1. Introduction
  • 2. Analytic Potential Theory
  • 3. Markov Processes
  • 4. Stochastic Calculus
  • 5. Probabilistic Interpretations
  • References
  • Introduction to Random Walks on Noncommutative Spaces
  • 1. Introduction
  • 2. Noncommutative Spaces and Random Variables
  • 3. Quantum Bernoulli Random Walks
  • 4. Bialgebras and Group Algebras
  • 5. Random Walk on the Dual of SU(2)
  • 6. Random Walks on Duals of Compact Groups
  • 7. The Case of SU(n)
  • 8. Choquet-Deny Theorem for Duals of Compact Groups
  • 9. The Martin Compactification of the Dual of SU(2)
  • 10. Central Limit Theorems for the Bernoulli Random Walk
  • 11. The Heisenberg Group and the Noncommutative Brownian Motion
  • 12. Dilations for Noncompact Groups
  • 13. Pitman's Theorem and the Quantum Group SU[subscript q](2)
  • References
  • Interactions between Quantum Probability and Operator Space Theory
  • 1. Introduction
  • 2. Completely Positive Maps
  • 3. Concrete Operator Spaces and Completely Bounded Maps
  • 4. Ruan's Theorem: Abstract Operator Spaces
  • 5. Complex Interpolation and Operator Hilbert Spaces
  • 6. Vector-valued Noncommutative L[subscript p]-spaces
  • 7. Noncommutative Khintchine Type Inequalities
  • 8. Embedding of OH into Noncommutative L[subscript 1]
  • References
  • Dirichlet Forms on Noncommutative Spaces
  • 1. Introduction
  • 2. Dirichlet Forms on C*-algebras and KMS-symmetric Semigroups
  • 3. Dirichlet Forms in Quantum Statistical Mechanics
  • 4. Dirichlet Forms and Differential Calculus on C*-algebras
  • 5. Noncommutative Potential Theory and Riemannian Geometry
  • 6. Dirichlet Forms and Noncommutative Geometry
  • 7. Appendix
  • 8. List of Examples
  • References
  • Applications of Quantum Stochastic Processes in Quantum Optics
  • 1. Quantum Probability
  • 2. Conditional Expectations
  • 3. Quantum Stochastic Calculus
  • 4. Quantum Filtering
  • References
  • Quantum Walks
  • Part I. Discrete-Time Quantum Walks
  • 1. Limit Theorems
  • 2. Disordered Case
  • 3. Reversible Cellular Automata
  • 4. Quantum Cellular Automata
  • 5. Cycle
  • 6. Absorption Problems
  • Part II. Continuous-Time Quantum Walks
  • 7. One-Dimensional Lattice
  • 8. Tree
  • 9. Ultrametric Space
  • 10. Cycle
  • References
  • Index

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