  Open quantum systems that interact with structured reservoirs exhibit
non-Markovian dynamics. We present a quantum jump method for treating the
dynamics of such systems. This approach is a generalization of the standard
Monte Carlo Wave Function (MCWF) method for Markovian dynamics. The MCWF method
identifies decay rates with jump probabilities and fails for non-Markovian
systems where the time-dependent rates become temporarily negative. Our
non-Markovian quantum jump (NMQJ) approach circumvents this problem and
provides an efficient unravelling of the ensemble dynamics.
