PUB - Publikationen an der Universität Bielefeld

The aim of this thesis is to develop an initial state characterization for heavy-ion collisions as well as a characterization of fluctuations arising from the initial-state energy density and their propagation into the final state.

In the first main part of the thesis we will set the stage and introduce the physics addressed in heavy-ion collisions and introduce different initial state models, namely the Glauber and Saturation model. Then we will derive the Boltzmann equation and introduce a numerical framework to solve it in two dimensions for an ideal gas of massless particles. The motivation for this new framework is the following: In small systems or peripheral collisions the number of interactions is small and the applicability of hydrodynamics is still under debate.

The second main part will study how fluctuations in anisotropic transverse flow occur due to a finite number of rescatterings during the system evolution within the numerical approach. Initial geometries from a Monte Carlo Glauber model are used to study how flow coefficients fluctuate about their mean value for a given initial-state eccentricity. Additionally we study for the first time how the distributions of the second and third event planes of anisotropic flow about their participant planes in the initial state evolve with the mean number of rescatterings in the system.

In the third part of the thesis we will study the generation of an anisotropic flow signal and spatial eccentricities in more detail, especially at early times using different particle-based transport approaches and a fixed initial condition. We study the onset of anisotropic flow as a function of the number of rescatterings from the few-rescatterings case to the hydrodynamic regime using a power-law ansatz and an exponent varying with the number of rescatterings. The numerical results are compared to semi-analytical calculations based on an expansion in powers of time and cross section in the few-rescatterings regime. Additionally, we will test the effectiveness of the ``escape mechanism'' to create anisotropic flow in two numerical scenarios with a $2\rightarrow 2$ and $2\rightarrow 0$ collision kernel respectively, and we compare the results to analytical calculations using only the loss term in the Boltzmann equation. This reveals that the even flow harmonics behave similarly, while the odd ones show a significant difference.

The fourth part of this thesis develops a general decomposition of an initial state density profile ensemble using an average state and independent orthonormal fluctuation modes. Event-by-event fluctuations are encoded in the modes forming a basis. Using Glauber and Saturation type initial conditions, we quantify different types and probabilities of event-by-event fluctuations and their impact on initial-state characteristics. Using dynamical simulations within K{\o}MP{\o}ST and MUSIC, we investigate the impact of single modes on final-state observables and their correlations. A comparison to event-by-event simulations is used to quantify the accuracy of the mode-by-mode approach.