Far-from-equilibrium universal scaling dynamics in ultracold atomic systems and heavy-ion collisions

Classification and understanding of scaling solutions in closed quantum systems far from thermal equilibrium, known as nonthermal fixed points, are one of the open problems in nonequilibrium quantum many-body theory. The usual method involves searching for possible self-similar solutions to a (nonperturbative) evolution equation, e.g., Boltzmann or Kadanoff-Baym, starting from a far-from-equilibrium initial condition. In this work, we develop an alternative approach based on the correspondence between scaling and fixed points of the renormalization group. Using an ultracold Bose gas as an example we show how possible far-from-equilibrium scaling solutions can be systematically obtained by solving fixed-point renormalization-group equations. In the second part of this thesis, we investigate dynamics preceding a fully developed self-similar evolution. We use the Hamiltonian formulation of kinetic theory to perform a stability analysis of nonthermal fixed points in an expanding non-Abelian plasma characterized by the Fokker-Planck collision kernel. Employing an adiabatic expansion we develop a perturbation theory, which at next-to-leading order allows us to derive stability equations for scaling exponents and obtain the Lyapunov relaxation rates associated with a nonthermal fixed point.