Quantum Potential Theory

  • Authors
  • Philippe Biane
  • Luc Bouten
  • Fabio Cipriani
  • Norio Konno
  • Nicolas Privault
  • Quanhua Xu
  • Uwe Franz
  • Michael Schürmann

Part of the Lecture Notes in Mathematics book series (LNM, volume 1954)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Pages 1-2
  3. Nicolas Privault
    Pages 3-59
  4. Fabio Cipriani
    Pages 161-276
  5. Norie Konno
    Pages 309-452
  6. Back Matter
    Pages 453-463

About this book

Introduction

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.

Keywords

Dirichlet forms Martin and Poissin boundary Potential theory Quantum Markov processes and semigroups Quantum filtering problem Random walks and quantum walks quantum physics

Editors and affiliations

  • Uwe Franz
    • 1
    • 2
  • Michael Schürmann
    • 3
  1. 1.Département de mathématiques de BesanconUniversité de Franche-ComtéBesancon cedexFrance
  2. 2.Graduate School of Information SciencesTohoku UniversitySendaiJapan
  3. 3.Institut für Mathematik und InformatikErnst-Moritz-Arndt-Universität GreifswaldGreifswaldGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-69365-9
  • Copyright Information Springer Berlin Heidelberg 2008
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-69364-2
  • Online ISBN 978-3-540-69365-9
  • Series Print ISSN 0075-8434
  • About this book