Probability Theory and Related Fields

, Volume 83, Issue 4, pp 489–508

Quantum Poisson processes and dilations of dynamical semigroups

  • Alberto Frigerio
  • Hans Maassen


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 algebraMn 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 semigroupetL of transition operators on (Mn, π) has generator
whereu is an arbitrary unitary element of the centraliser of (Mn⊗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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