Universal dynamics and thermalization in isolated quantum systems

The goal of this work is to explore the relaxation dynamics of isolated quantum systems driven out of equilibrium, focusing on nonequilibrium phenomena emerging on the way to thermal equilibrium. We study close-to-equilibrium states relaxing to thermal equilibrium directly as well as far-from-equilibrium states approaching a transient regime characterized by a self-similar time evolution. One of the most persistent challenges concerns the thermalization process of the quark-gluon plasma in heavy-ion collisions. We address this issue by investigating the equilibration process of the quark-meson model, an effective low-energy theory of quantum chromodynamics (QCD) that captures important features of QCD including the chiral phase transition. Our simulations probe the approach of quantum thermal equilibrium, characterized by the emergence of Bose-Einstein and Fermi-Dirac distribution functions, in different regions of the phase diagram. We find additional light fermionic degrees of freedom in the crossover region of the quasiparticle excitation spectrum. A remarkable feature of isolated quantum systems is that far-from-equilibrium states can approach nonthermal fixed points, where the dynamics becomes self-similar and universal across disparate physical systems. We study the infrared nonthermal fixed point by investigating the scaling properties of distribution functions in a relativistic scalar field theory as well as a spin-1 Bose gas. For the scalar field theory we also compute the effective four-vertex and unequal-time two-point correlation functions entailing the nonthermal properties of the system in terms of a strongly violated fluctuation-dissipation theorem. In the spin-1 Bose gas quickly emerging long-range correlations indicate the formation of a condensate out of equilibrium