  Nonthermal fixed points of the dynamics of a dilute degenerate Bose gas far
from thermal equilibrium are analyzed in two and three spatial dimensions.
Universal power-law distributions, previously found within a nonperturbative
quantum-field theoretical approach and recently shown to be related to vortical
dynamics and superfluid turbulence [Phys. Rev. B 84, 020506(R) (2011)], are
studied in detail. The results imply an interpretation of the scaling behavior
in terms of independent vortex excitations of the superfluid and show that the
statistics of topological excitations can be described in the framework of wave
turbulence. The particular scaling exponents observed in the single-particle
momentum distributions are found to be consistent with irreversibility as well
as conservation laws obeyed by the wave interactions. Moreover, long-wavelength
acoustic excitations of the vortex-bearing condensate, driven by vortex
annihilations, are found to follow a nonthermal power law. Considering vortex
correlations in a statistical model, the long-time departure from the
nonthermal fixed point is related to vortex-antivortex pairing. The studied
nonthermal fixed points are accessible in cold-gas experiments. The results
shed light on fundamental aspects of superfluid turbulence and have strong
potential implications for related phenomena, e.g., in early-universe inflation
or quark-gluon plasma dynamics.
