EPL, 85 (2009) 50004
DOI: 10.1209/0295-5075/85/50004

Stochastic jump processes for non-Markovian quantum dynamics

H.-P. Breuer¹ and J. Piilo<sup>2

1</sup>   Physikalisches Institut, Universität Freiburg - Hermann-Herder-Strasse 3, D-79104 Freiburg, Germany, EU
²   Department of Physics and Astronomy, University of Turku - FI-20014 Turun yliopisto, Finland, EU

breuer@physik.uni-freiburg.de
jyrki.piilo@utu.fi

received 12 December 2008; accepted in final form 13 February 2009; published March 2009
published online 17 March 2009

Abstract
It is shown that non-Markovian master equations for an open system which are local in time can be unravelled through a piecewise deterministic quantum jump process in its Hilbert space. We derive a stochastic Schrödinger equation that reveals how non-Markovian effects are manifested in statistical correlations between different realizations of the process. Moreover, we demonstrate that possible violations of the positivity of approximate master equations are closely connected to singularities of the stochastic Schrödinger equation, which could lead to important insights into the structural characterization of positive non-Markovian equations of motion.

PACS
03.65.Yz - Decoherence; open systems; quantum statistical methods.
42.50.Lc - Quantum fluctuations, quantum noise, and quantum jumps.

© EPLA 2009