Marco Schweizer

In all relevant real world applications quantum systems are exposed to their environment possessing an overwhelming number of degrees of freedom so that the exact evolution of the composite system becomes impossible to solve numerically. A coarsegrained approach in the spirit of thermodynamics that focuses only on the relevant features of the system was developped 1; the environment is treated thermodynamically and most strikingly dynamically while being coupled to the quantum system of interest. The latter is described by a highly nonlinear quantum master equation with many appealing thermodynamic properties as opposed to linear frameworks. In the thesis it is shown that despite of the nonlinear structure problems can be solved by a Monte-Carlo technique. In addition, common stochastic integration schemes are extended and improved to obtain higher order of convergence. While results are presented to the prototypical toy model of a simple qubit coupled to a classical heat bath, extensions are highlighted to treat much more involved problems.