  Non-equilibrium conditions give rise to classes of universally evolving
configurations of quantum-many body systems at non-thermal fixed points. While
the fixed point and thus full scaling in space and time is generically reached
at very long evolution times, we propose that systems can show prescaling much
earlier in time, in particular, on experimentally accessible time scales.
During the prescaling evolution, some well-measurable properties of spatial
correlations already scale with the universal exponents of the fixed point
while others still show scaling violations. Prescaling is characterized by the
evolution obeying conservation laws associated with the remaining symmetry
which also defines the universality class of the asymptotically reached
non-thermal fixed point. Here we consider $N=3$ species of spatially uniform
three-dimensional Bose gases, with identical inter- and intra-species
interactions. During prescaling, the full $U(N)$ symmetry of the model is
broken to $U(N-1)$ while the conserved transport, reflecting explicit and
emerging symmetries, leads to the buildup of rescaling quasicondensate
distributions.
