Probability Theory and Related Fields

, Volume 126, Issue 2, pp 289–306 | Cite as

Transience and recurrence of quantum Markov semigroups

  • Franco Fagnola
  • Rolando Rebolledo

Abstract.

 This article introduces a concept of transience and recurrence for a Quantum Markov Semigroup and explores its main properties via the associated potential. We show that an irreducible semigroup is either recurrent or transient and characterize transient semigroups by means of the existence of non trivial superharmonic operators.

Keywords

Main Property Markov Semigroup Irreducible Semigroup Quantum Markov Semigroup 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Franco Fagnola
    • 1
  • Rolando Rebolledo
    • 2
  1. 1.Università degli Studi di Genova, Dipartimento di Matematica, via Dodecaneso 35, I-16146 Genova
  2. 2.Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Casilla 306, Santiago 22, Chile. e-mail: rrebolle@puc.clCL

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