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Bose condensation far from equilibrium

The formation of Bose condensates far from equilibrium can play an important role in our understanding of collision experiments of heavy nuclei or for the evolution of the early universe. In the relativistic quantum world particle number changing processes can counteract Bose condensation, and there is a considerable debate about the relevance of this phenomenon in this context. We show that the involved question of Bose condensation from initial over-population can be answered for the example of scalar field theories. Condensate formation occurs as a consequence of an inverse particle cascade with a universal power-law spectrum. This particle transport towards low momenta is part of a dual cascade, in which energy is also transfered by weak wave turbulence towards higher momenta. To highlight the importance of number changing processes for the subsequent decay of the condensate, we also compare to non-relativistic theories with exact number conservation. We discuss the relevance of these results for nonabelian gauge theories.