PUB - Publikationen an der Universität Bielefeld

The experimentally obtained anisotropic flow coefficients represent one of the main observables in the field of ultra-relativistic heavy-ion collisions (HIC), which can be reproduced by theoretical descriptions from a realistically modelled initial stage.

In this thesis we see that it is possible - already by considering a few collisions - to translate anisotropies of the initial stage in position space into anisotropies of momentum space which are similar in form to those of hydrodynamics. Relativistic hydrodynamics is the theoretical model to describe the small droplet of ultra-dense partonic matter (quark-gluon plasma, QGP) generated in HIC. However, we show that the anisotropic flow coefficients are not uniquely generated by collectivity effects. In this respect, our approach offers an alternative to the hydrodynamic description in the few collision regime, which is expected with regard to small and diluted systems.

More precisely, we provide a systematic expansion from free-streaming to first order in inverse Knudsen number, which allows for the consistent consideration of few collisions. The latter are taken into account by the elastic collision kernel of the relativistic Boltzmann equation in our approach to best describe the dynamics of the interacting system.

Our analytical calculations give concrete expressions for the time-dependent anisotropic flow coefficients as response to the initial geometry profile of the system generated in HIC.

The structured comparison of our analytical model with for our purposes adapted numerical transport code, which simulates massless particles in two dimensions, shows that our results are in excellent agreement in the few collision regime. Besides validating our analytical approach, we also confirm that the escape mechanism provides the dominant contribution to the flow signal within the few collision regime.

Finally, the extension of our analytical escape mechanism to the description of massive particles in three dimensions allows a step towards the description of Bottomonia, which fly through a system of massless particles and which, due to their properties, are considered as a probe of the initial stage of HIC.