  We investigate universal behavior of isolated many-body systems far from
equilibrium, which is relevant for a wide range of applications from ultracold
quantum gases to high-energy particle physics. The universality is based on the
existence of nonthermal fixed points, which represent nonequilibrium attractor
solutions with self-similar scaling behavior. The corresponding dynamic
universality classes turn out to be remarkably large, encompassing both
relativistic as well as nonrelativistic quantum and classical systems. For the
examples of nonrelativistic (Gross-Pitaevskii) and relativistic scalar field
theory with quartic self-interactions, we demonstrate that infrared scaling
exponents as well as scaling functions agree. We perform two independent
nonperturbative calculations, first by using classical-statistical lattice
simulation techniques and second by applying a vertex-resummed kinetic theory.
The latter extends kinetic descriptions to the nonperturbative regime of
overoccupied modes. Our results open new perspectives to learn from experiments
with cold atoms aspects about the dynamics during the early stages of our
universe.
