Final Activity Report Summary - QuantumGases (Quantum gases: understanding their dynamics and improving simulation methods) In the rapidly expanding field of cold atom research atoms that we used to thinking of as particles behave as a collective wave to a degree that was unknown before on a macroscopic scale since, historically, wave behaviour of particles was only well known for photons or tiny objects on the atomic scale. In recent years, some research components moved into a further direction, in which the atoms were dynamically caused to behave, again, in a particle-like manner as time progressed. They might then also revert back to a wave-like nature, and so forth. An example are the fast collisions of the wave-like Bose-Einstein condensates, in which scattered matter is best described again as particles, or single atoms. However, under the right conditions these scattered particles can begin to accumulate more around each other, eventually forming their own wave-like state again, which is called a phase grain. A hindrance here was that, in many cases, it was not possible to compute beforehand what dynamics would occur, or to perform calculations after the experiment to check whether what was seen corresponded to what was thought to be happening. The problem was that the standard quantum mechanical description did not fit in any computer, while more subtle methods fit but did not allow for long enough calculations to compare with most experiments. The aim of this project was to develop more cunning descriptions of these systems that would be computationally tractable and give results for long evolution. Such an improved description was indeed developed. This made possible to calculate the dynamics for much longer times and for a much broader class of problems than before. In fact, calculations for several cases were already made in the course of the project.