  The trapping of excitations in systems coupled to an environment allows to
study the quantum to classical crossover by different means. We show how to
combine the phenomenological description by a non-hermitian Liouville-von
Neumann Equation (LvNE) approach with the numerically exact path integral
Monte-Carlo (PIMC) method, and exemplify our results for a system of two
coupled two-level systems. By varying the strength of the coupling to the
environment we are able to estimate the parameter range in which the LvNE
approach yields satisfactory results. Moreover, by matching the PIMC results
with the LvNE calculations we have a powerful tool to extrapolate the
numerically exact PIMC method to long times.
