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Birkhäuser

Stochastic Analysis and Mathematical Physics

ANESTOC ’98 Proceedings of the Third International Workshop

  • Conference proceedings
  • © 2000

Overview

Editors:
  1. Rolando Rebolledo

    1. Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Santiago 22, Chile

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Part of the book series: Trends in Mathematics (TM)

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Table of contents (11 papers)

  1. Front Matter

    Pages i-ix
    Download chapter PDF

  2. Exponential L 2-Convergence of Some Quantum Markov Semigroups Related to Birth-and-Death Processes

    • Raffaella Carbone
    Pages 1-22

  3. Conservativity of Quantum Dynamical Evolution Systems

    • A. M. Chebotarev, J. C. García, R. Quezada
    Pages 23-31

  4. Upper Bounds on Bogolubov’s Inner Product: Quantum Systems of Anharmonic Oscillators

    • M. Corgini
    Pages 33-39

  5. Bernstein Processes Associated with a Markov Process

    • A. B. Cruzeiro, Liming Wu, J. C. Zambrini
    Pages 41-72

  6. A Simple Singular Quantum Markov Semigroup

    • Franco Fagnola
    Pages 73-87

  7. On a Theory of Resonance in Quantum Mechanical Scattering

    • Claudio Fernández, Kalyan B. Sinha
    Pages 89-95

  8. Representation of the q-Deformed Oscillator

    • Alain Guichardet
    Pages 97-99

  9. On the Existence of Exponentials of Quadratic Polynomials of Field Operators on Fock Space

    • Erik B. Nielsen, Ole Rask
    Pages 101-107

  10. The Wave Map of Feller Semigroups

    • Rolando Rebolledo
    Pages 109-121

  11. On the Korovkin Property and Feller Semigroups

    • Jan A. Casteren
    Pages 123-154

  12. An Example of the Singular Coupling Limit

    • Wilhelm von Waldenfels
    Pages 155-166
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About this book

The seminar on Stochastic Analysis and Mathematical Physics started in 1984 at the Catholic University of Chile in Santiago and has been an on­ going research activity. Since 1995, the group has organized international workshops as a way of promoting a broader dialogue among experts in the areas of classical and quantum stochastic analysis, mathematical physics and physics. This volume, consisting primarily of contributions to the Third Inter­ national Workshop on Stochastic Analysis and Mathematical Physics (in Spanish ANESTOC), held in Santiago, Chile, in October 1998, focuses on an analysis of quantum dynamics and related problems in probability the­ ory. Various articles investigate quantum dynamical semigroups and new results on q-deformed oscillator algebras, while others examine the appli­ cation of classical stochastic processes in quantum modeling. As in previous workshops, the topic of quantum flows and semigroups occupied an important place. In her paper, R. Carbone uses a spectral type analysis to obtain exponential rates of convergence towards the equilibrium of a quantum dynamical semigroup in the £2 sense. The method is illus­ trated with a quantum extension of a classical birth and death process. Quantum extensions of classical Markov processes lead to subtle problems of domains. This is in particular illustrated by F. Fagnola, who presents a pathological example of a semigroup for which the largest * -subalgebra (of the von Neumann algebra of bounded linear operators of £2 (lR+, IC)), con­ tained in the domain of its infinitesimal generator, is not a-weakly dense.

Editors and Affiliations

  • Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Santiago 22, Chile

    Rolando Rebolledo

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