Probability Theory and Related Fields

, Volume 83, Issue 4, pp 489–508 | Cite as

Quantum Poisson processes and dilations of dynamical semigroups

  • Alberto Frigerio
  • Hans Maassen
Article

Summary

The notion of a quantum Poisson process over a quantum measure space is introduced. This process is used to construct new quantum Markov processes on the matrix algebraM n with stationary faithful state π. If (ℳ, μ) is the quantum measure space in question (ℳ a von Neumann algebra and μ a faithful normal weight), then the semigroupe tL of transition operators on (M n , π) has generator
whereu is an arbitrary unitary element of the centraliser of (M n ⊗ℳ,φ⊗μ).

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Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Alberto Frigerio
    • 1
  • Hans Maassen
    • 2
  1. 1.Dipartimento di Matematica e InformaticaUniversita di UdineUdineItaly
  2. 2.Mathematisch InstituutKatholieke Universiteit NijmegenNijmegenThe Netherlands

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