Transience and recurrence of quantum Markov semigroups

 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. 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