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Transience and recurrence of quantum Markov semigroups
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  • Published: June 2003

Transience and recurrence of quantum Markov semigroups

  • Franco Fagnola1 &
  • Rolando Rebolledo2 

Probability Theory and Related Fields volume 126, pages 289–306 (2003)Cite this article

  • 198 Accesses

  • 36 Citations

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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.

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Authors and Affiliations

  1. Università degli Studi di Genova, Dipartimento di Matematica, via Dodecaneso 35, I-16146 Genova, , , , ,

    Franco Fagnola

  2. Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Casilla 306, Santiago 22, Chile. e-mail: rrebolle@puc.cl, , , , , , CL

    Rolando Rebolledo

Authors
  1. Franco Fagnola
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  2. Rolando Rebolledo
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Additional information

Received: 27 January 2003 / Revised version: 19 February 2003 / Published online: 12 May 2003

This research has been partially supported by the ``Cátedra Presidencial en Análisis Cualitativo de Sistemas Dinámicos Cuánticos'', DIPUC, FONDECYT project 1030552, MIUR program ``Probabilità Quantistica e Applicazioni'', 2003-2004 and MECESUP PUC 0103.

Mathematics Subject Classification (2000): 60J45, 81S25, 60J99, 37A50, 47A40

Key words or phrases: Quantum Markov semigroups – Potential theory – Markov processes

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Fagnola, F., Rebolledo, R. Transience and recurrence of quantum Markov semigroups. Probab. Theory Relat. Fields 126, 289–306 (2003). https://doi.org/10.1007/s00440-003-0268-0

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  • Issue Date: June 2003

  • DOI: https://doi.org/10.1007/s00440-003-0268-0

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Keywords

  • Main Property
  • Markov Semigroup
  • Irreducible Semigroup
  • Quantum Markov Semigroup
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