Stochastic jump processes for non-Markovian quantum dynamics

¹  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

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

Received: 12 December 2008
Accepted: 13 February 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.