What if the Milky Way was a quantum-mechanical object?

The formation and evolution of cosmic structures provides a link between the physics of the largest and smallest objects: The formation history and the properties of cosmic structures depend crucially on the elementary properties of dark matter particles and provide a laboratory for properties inaccessible by terrestial experiments. In this research programme we focus on axions and axion-like particles as viable and physically well-motivated dark matter particle candidate, whose dynamics is quantum-mechanical, due to their very large de Broglie-wave length. In particular, our proposal is centered on the formation of self-gravitating, quantum-mechanical systems and their equilibrium properties, as well as their observable signatures. In doing that, we intend to go much beyond the well-known Gross-Pitaevskii-equation, by relaxing on the requirement of perfect coherence and allowing finite temperatures.