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Periodically-driven quantum systems make it possible to reach stationarystates with new emerging properties. However, this process is notoriouslydifficult in the presence of interactions because continuous energy exchangesgenerally boil the system to an infinite temperature featureless state. Here,we describe how to reach nontrivial states in a periodically-kickedGross-Pitaevskii disordered system. One ingredient is crucial: both disorderand kick strengths should be weak enough to induce sufficiently narrow andwell-separated Floquet bands. In this case, inter-band heating processes arestrongly suppressed and the system can reach an exponentially long-livedprethermal plateau described by the Rayleigh-Jeans distribution. Saliently, thesystem can even undergo a wave condensation process when its initial state hasa sufficiently low total quasi-energy. These predictions could be tested innonlinear optical experiments or with ultracold atoms.

Prethermalization and wave condensation in a nonlinear disordered Floquet system