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A pathwise ergodic theorem for quantum trajectories

B Kümmerer et al 2004 J. Phys. A: Math. Gen. 37 11889-11896   doi: 10.1088/0305-4470/37/49/008  Help

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B Kümmerer1 and H Maassen2
1 Fachbereich Mathematik, Technische Universität Darmstadt, Schlossgartenstraße 7, D-64 289 Darmstadt, Germany
2 Mathematisch Instituut, Radboud Universiteit Nijmegen, Toernooiveld 1, 6525 ED Nijmegen, The Netherlands
E-mail: kuemmerer@mathematik.tu-darmstadt.de and maassen@math.ru.nl

Abstract. If the time evolution of an open quantum system approaches equilibrium in the time mean, then on any single trajectory of any of its unravellings the time-averaged state approaches the same equilibrium state with probability 1. In the case of multiple equilibrium states, the quantum trajectory converges in the mean to a random choice from these states.

PACS numbers: 02.50.Ga, 02.70.Lq, 03.65.Bz, 42.50.Lc

Print publication: Issue 49 (10 December 2004)
Received 25 June 2004, in final form 18 October 2004
Published 24 November 2004

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