Weak wave turbulence as a precursor to universal coarsening

We study particle transport during the relaxation of an isolated low-energy Bose gas from a far-from-equilibrium incoherent state towards a condensed state. We focus on the initial stage of particle transport to low momenta, before the emergence of a condensate. In terms of the gas density n and interatomic s-wave scattering length a, we find the time for incoherent particle transport is set by 1/(na)², in contrast to the collisional timescale 1/(na²). We observe an inverse particle cascade with the momentum distribution developing a power law tail with exponent γ≈2.4(2). Both of these observations are signatures of Weak Wave Turbulence (WWT). Finally, we study where the WWT scaling breaks down and the transition to universal coarsening, for which the relaxation time is independent of both n and a.