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Abstract

We investigate several aspects of the non-equilibrium dynamics of non-abelian gauge theories, relevant to the problem of thermalization in relativistic heavy-ion collision experiments. We perform numerical simulations in the framework of classical-statistical lattice gauge theory as a first principle approach to study the non-equilibrium dynamics of weakly coupled yet strongly correlated non-abelian plasmas. The numerical studies are complemented by analytic considerations in the framework of kinetic theory and two-particle irreducible effective action techniques. Following a general introduction, the theoretical framework and the range of validity of the employed approximations is discussed.

The first main part of this thesis is concerned with the study of thermalization of non-abelian plasmas in Minkowski space. We establish by numerical studies, that the thermalization process is governed by a turbulent cascade towards the ultraviolet in the regime where quantum corrections can safely be neglected. The dynamics of the universal turbulent attractor is characterized by a self-similar evolution in time and we extract the universal scaling exponents and scaling functions. It is shown that the scaling exponents observed in numerical simulations agree with the ones extracted from a scaling analysis in the kinetic theory framework. In the second main part of this thesis, we investigate the non-equilibrium dynamics of in- stabilities. We investigate analytically the unstable dynamics of coherent non-abelian gauge fields and compare our findings with the results from classical-statistical lattice simulations. The simulations demonstrate the phenomenon of non-linear self-amplification of the instability due to interactions of unstable modes. The non-linear dynamics of instabilities is discussed both analytically and numerically for the example of an anisotropically expanding scalar field theory, with a particular emphasis on the role of the anisotropic expansion of the system.

The third part of this work focuses on the non-equilibrium dynamics of anisotropically expanding non-abelian plasmas as encountered in heavy-ion collisions at ultra-relativistic energies. While our simulations indicate the importance of plasma instabilities and free streaming for the early stages of the evolution, we discover that the subsequent dynamics is again governed by a universal turbulent attractor. Most remarkably, the universal scaling exponents which characterize the self-similar evolution in the turbulent regime can be explained by elastic scattering processes.