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We investigate universal behavior of isolated many-body systems far fromequilibrium, which is relevant for a wide range of applications from ultracoldquantum gases to high-energy particle physics. The universality is based on theexistence of nonthermal fixed points, which represent nonequilibrium attractorsolutions with self-similar scaling behavior. The corresponding dynamicuniversality classes turn out to be remarkably large, encompassing bothrelativistic as well as nonrelativistic quantum and classical systems. For theexamples of nonrelativistic (Gross-Pitaevskii) and relativistic scalar fieldtheory with quartic self-interactions, we demonstrate that infrared scalingexponents as well as scaling functions agree. We perform two independentnonperturbative calculations, first by using classical-statistical latticesimulation techniques and second by applying a vertex-resummed kinetic theory.The latter extends kinetic descriptions to the nonperturbative regime ofoveroccupied modes. Our results open new perspectives to learn from experimentswith cold atoms aspects about the dynamics during the early stages of ouruniverse.

Universal self-similar dynamics of relativistic and nonrelativistic field theories near nonthermal fixed points